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How many different arrangements of five different consonants of the English alphabet are possible such that the letters are in alphabetical order in each arrangement?
  • a)
    53130
  • b)
    20349
  • c)
    6375600
  • d)
    2441880
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
How many different arrangements of five different consonants of the En...
Five different consonants can be chosen in 21C5 ways.
Since the order of the letters is fixed i.e. alphabetical order, the consonants can be arranged in only one way once they are selected.
e.g. if the consonants B, G, L, P and S are selected, there is only alphabetical order possible i.e. BGLPS.
Required total number of arrangements = 21C5 = 20349
Hence, option 2.
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Community Answer
How many different arrangements of five different consonants of the En...
To solve this problem, we need to consider the number of arrangements of five different consonants of the English alphabet such that the letters are in alphabetical order in each arrangement.

Breaking down the problem, we can consider the process step by step:

Step 1: Selecting the consonants
We need to select five different consonants from the English alphabet. Since there are 21 consonants in the English alphabet, we can do this in "21 choose 5" ways, which can be denoted as C(21,5) or 21C5.

Step 2: Arranging the selected consonants
Once we have selected the five consonants, we need to arrange them in alphabetical order. Since the letters have to be in alphabetical order, there is only one way to arrange them.

Step 3: Calculating the total number of arrangements
To find the total number of arrangements, we need to multiply the number of ways to select the consonants by the number of ways to arrange them.

C(21,5) = 21! / (5! * (21-5)!)
= (21 * 20 * 19 * 18 * 17) / (5 * 4 * 3 * 2 * 1)
= 20349

Therefore, the correct answer is option B) 20349.

Visually appealing breakdown:

Step 1: Selecting the consonants
- There are 21 consonants in the English alphabet.
- We need to select 5 consonants.
- The number of ways to select 5 consonants out of 21 is C(21,5) or 21C5.

Step 2: Arranging the selected consonants
- Once we have selected the 5 consonants, we need to arrange them in alphabetical order.
- Since the letters have to be in alphabetical order, there is only one way to arrange them.

Step 3: Calculating the total number of arrangements
- To find the total number of arrangements, we multiply the number of ways to select the consonants by the number of ways to arrange them.
- C(21,5) = 20349.

Therefore, the correct answer is option B) 20349.
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The chief scientist of a major vaccine producing company has the responsibility to keep the formula of the vaccine confidential. He stores the formula in his e-device with 3 consecutive locks, all of which need to be unlocked to access the formula. The first of the 3 locks is a pattern lock, the second one is a numeric lock and the third and final one is an alphanumeric lock. The pattern lock is in the form of a regular hexagon with 6 distinct vertices A1, A2, A3, A4, A5, A6, in that order. One needs to connect all the 6 vertices one after the another in any random order connecting each vertex only once and only one order of connecting the 6 vertices exists which will unlock the first lock. The numeric lock has a code of ABC, where A, B and C are single digit natural numbers. A is a multiple of 2. B is a multiple of 3, C is a multiple of 4 but not equal to A.The alphanumeric lock has a code MNPQRS, where M and N are alphabets and P, Q, R and S are digits. M and N have to be consecutive vowels or consecutive consonants, not necessarily in order. Two alphabets are said to be consecutive vowels if both of them are vowels and they are consecutive when all the 5 vowels are written in alphabetical order. For example, E and I are consecutive vowels, but A and O are not. Two alphabets are said to be consecutive consonants if both of them are consonants and they are consecutive when all the 21 consonants are written in alphabetical order. For example, D and F are consecutive consonants but D and V are not. For example, M and N can be A and E respectively or E and A respectively. P is equal to Base-Ten-Index of M. Q is equal to the Base-Ten-Index of N. R and S can only take binary values, that is, 0 or 1.Base-Ten-Index of an alphabet = Index of alphabet % 10, where Index of an alphabet is its position when all alphabets from A to Z are arranged alphabetically and a%b is the remainder when a is divided by b.For example, Base-Ten-Index of J = 10 = 0 , Base-Ten-Index of M = 13 = 3.The chief scientist can only set passwords/patterns which follow all of the conditions mentioned above.Based on the information given above, answer the questions that follow.Q.How many alphanumeric codes for the third lock are possible which necessarily have an A as one of the alphabets in the code?

The chief scientist of a major vaccine producing company has the responsibility to keep the formula of the vaccine confidential. He stores the formula in his e-device with 3 consecutive locks, all of which need to be unlocked to access the formula. The first of the 3 locks is a pattern lock, the second one is a numeric lock and the third and final one is an alphanumeric lock. The pattern lock is in the form of a regular hexagon with 6 distinct vertices A1, A2, A3, A4, A5, A6, in that order. One needs to connect all the 6 vertices one after the another in any random order connecting each vertex only once and only one order of connecting the 6 vertices exists which will unlock the first lock. The numeric lock has a code of ABC, where A, B and C are single digit natural numbers. A is a multiple of 2. B is a multiple of 3, C is a multiple of 4 but not equal to A.The alphanumeric lock has a code MNPQRS, where M and N are alphabets and P, Q, R and S are digits. M and N have to be consecutive vowels or consecutive consonants, not necessarily in order. Two alphabets are said to be consecutive vowels if both of them are vowels and they are consecutive when all the 5 vowels are written in alphabetical order. For example, E and I are consecutive vowels, but A and O are not. Two alphabets are said to be consecutive consonants if both of them are consonants and they are consecutive when all the 21 consonants are written in alphabetical order. For example, D and F are consecutive consonants but D and V are not. For example, M and N can be A and E respectively or E and A respectively. P is equal to Base-Ten-Index of M. Q is equal to the Base-Ten-Index of N. R and S can only take binary values, that is, 0 or 1.Base-Ten-Index of an alphabet = Index of alphabet % 10, where Index of an alphabet is its position when all alphabets from A to Z are arranged alphabetically and a%b is the remainder when a is divided by b.For example, Base-Ten-Index of J = 10 = 0 , Base-Ten-Index of M = 13 = 3.The chief scientist can only set passwords/patterns which follow all of the conditions mentioned above.Based on the information given above, answer the questions that follow.Q.Given below is a list of patterns/passwords, some of which are in accordance with the rules mentioned and some are not. The chief scientist can use any combination of valid patterns/passwords from the following to lock the e-device. What is the total number of ways in which he can do so?Pattern:(1) A1 A2 A5 A6 A5 A2 A4 (2) A1 A2 A3 A4 A5 A6 (3) A6 A5 A4 A3 A2 A1 (4) A1 A6 A5 A2 A4Numeric password:(1) 234 (2) 434 (3) 298 (4) 634 (5) 894 (6) 230 (7) 638Alphanumeric password:(1) AE1500 (2) CD3410 (3) HJ8000 (4)QP7600 (5) AB1211 (6) YZ4600 Correct answer is '40'. Can you explain this answer?

A lock is guarded by a security code that serves as the password. The code is in the following form:Where a, b, c, d and g are numbers and e, f are alphabets. The following information is also known about the respective characters:1. a is a prime number from 1 to 10.2. The 2-digit number bc is also a prime number such that b = a + 1.3. d = bc % a, that is, d is the remainder when the 2-digit number bc is divided by a.4. e is the alphabet at the index of n, alphabet[n], where n is the highest number of occurrences of any digit(0 to 9) among a,b,c,d. Here,alphabet[1] = A, alphabet[2] = B,..., alphabet[26] = Z.5. f is the alphabet either preceding or succeeding the alphabet e when all English alphabets are arranged alphabetically.6. g is the remainder when the sum of digits a, b, c and d is divided by 10. g = (a+b+c+ d).Based on the information given above, answer the questions that follow.If we consider all possible codes, how many distinct alphabets appear at least once in any of the codes? Correct answer is '3'. Can you explain this answer?

A lock is guarded by a security code that serves as the password. The code is in the following form:Where a, b, c, d and g are numbers and e, f are alphabets. The following information is also known about the respective characters:1. a is a prime number from 1 to 10.2. The 2-digit number bc is also a prime number such that b = a + 1.3. d = bc % a, that is, d is the remainder when the 2-digit number bc is divided by a.4. e is the alphabet at the index of n, alphabet[n], where n is the highest number of occurrences of any digit(0 to 9) among a,b,c,d. Here,alphabet[1] = A, alphabet[2] = B,..., alphabet[26] = Z.5. f is the alphabet either preceding or succeeding the alphabet e when all English alphabets are arranged alphabetically.6. g is the remainder when the sum of digits a, b, c and d is divided by 10. g = (a+b+c+ d).Based on the information given above, answer the questions that follow.If it is given that no vowel can be used as an alphabet and no digit should be a multiple of 4, how many codes are possible? Correct answer is '2'. Can you explain this answer?

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How many different arrangements of five different consonants of the English alphabet are possible such that the letters are in alphabetical order in each arrangement?a)53130b)20349c)6375600d)2441880Correct answer is option 'B'. Can you explain this answer?
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