A telecom company has decided to come up with new sim cards. It got the permission that it could assign its customers ten-digit numbers with the constraint that the numbers should start with 7809 and the remaining 6 digits can be selected from all 10 digits, without repetition such that they appear in the sim card number in ascending order. Find the maximum number of sim card numbers the company can come up with.a)210b)420c)1260d)5040Correct answer is option 'A'. Can you explain this answer?

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A telecom company has decided to come up with new sim cards. It got the permission that it could assign its customers ten-digit numbers with the constraint that the numbers should start with 7809 and the remaining 6 digits can be selected from all 10 digits, without repetition such that they appear in the sim card number in ascending order. Find the maximum number of sim card numbers the company can come up with.

a)
210
b)
420
c)
1260
d)
5040

Correct answer is option 'A'. Can you explain this answer?

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A telecom company has decided to come up with new sim cards. It got th...

Since the first 4 digits are fixed, all the arrangement and selection is to be done for the next 6 digits.

Now, we can select the 6 digits from all 10 digits, without repetition in ¹⁰c₆ ways.

Once, we select any set of 6 numbers, there is only one arrangement in which they appear in ascending order. So, for each possible selection, the number of ways = 1.

Hence, the total number of ways of selecting 10-digit numbers = ¹⁰C₆ × 1 = ¹⁰C₆ = ¹⁰C₄ =

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A telecom company has decided to come up with new sim cards. It got th...

Problem Analysis:
- The telecom company has to assign ten-digit numbers to its customers.
- The numbers should start with 7809, and the remaining 6 digits can be selected from all 10 digits without repetition.
- The selected digits should appear in ascending order in the sim card number.
- We need to find the maximum number of sim card numbers the company can come up with.

Solution:
To find the maximum number of sim card numbers, we need to consider the constraints and find the number of possible combinations.

Step 1: Selecting the remaining 6 digits
- The remaining 6 digits can be selected from all 10 digits without repetition.
- This can be done using combination formula: C(n, r) = n! / (r! * (n-r)!)
- In this case, n = 10 (total number of digits) and r = 6 (number of digits to be selected)
- So, C(10, 6) = 10! / (6! * (10-6)!)
= 10! / (6! * 4!)

Step 2: Arranging the selected digits in ascending order
- Once the 6 digits are selected, we need to arrange them in ascending order.
- The order of the digits matters, so we need to use permutation formula: P(n, r) = n! / (n-r)!
- In this case, n = 6 (number of digits selected) and r = 6 (number of digits to be arranged)
- So, P(6, 6) = 6! / (6-6)!
= 6! / 0!
= 6! / 1
= 6!

Step 3: Multiplying the combinations and permutations
- The number of possible combinations of selecting 6 digits from 10 is C(10, 6) = 10! / (6! * 4!)
- The number of possible permutations of arranging the selected 6 digits in ascending order is P(6, 6) = 6!
- To get the maximum number of sim card numbers, we need to multiply these two values.
- Max number of sim card numbers = C(10, 6) * P(6, 6)
= (10! / (6! * 4!)) * 6!

Calculating the Answer:
- Using the formula, we can calculate the maximum number of sim card numbers.
- Max number of sim card numbers = (10! / (6! * 4!)) * 6!
= (10 * 9 * 8 * 7) * (6 * 5 * 4 * 3 * 2 * 1)
= 210 * 720
= 151,200

Conclusion:
- The maximum number of sim card numbers the company can come up with is 151,200.
- The correct answer is option 'A' (210).

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A telecom company has decided to come up with new sim cards. It got th...

Since the first 4 digits are fixed, all the arrangement and selection is to be done for the next 6 digits.

Now, we can select the 6 digits from all 10 digits, without repetition in ¹⁰c₆ ways.

Once, we select any set of 6 numbers, there is only one arrangement in which they appear in ascending order. So, for each possible selection, the number of ways = 1.

Hence, the total number of ways of selecting 10-digit numbers = ¹⁰C₆ × 1 = ¹⁰C₆ = ¹⁰C₄ =

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A telecom company has decided to come up with new sim cards. It got the permission that it could assign its customers ten-digit numbers with the constraint that the numbers should start with 7809 and the remaining 6 digits can be selected from all 10 digits, without repetition such that they appear in the sim card number in ascending order. Find the maximum number of sim card numbers the company can come up with.a)210b)420c)1260d)5040Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A telecom company has decided to come up with new sim cards. It got the permission that it could assign its customers ten-digit numbers with the constraint that the numbers should start with 7809 and the remaining 6 digits can be selected from all 10 digits, without repetition such that they appear in the sim card number in ascending order. Find the maximum number of sim card numbers the company can come up with.a)210b)420c)1260d)5040Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A telecom company has decided to come up with new sim cards. It got the permission that it could assign its customers ten-digit numbers with the constraint that the numbers should start with 7809 and the remaining 6 digits can be selected from all 10 digits, without repetition such that they appear in the sim card number in ascending order. Find the maximum number of sim card numbers the company can come up with.a)210b)420c)1260d)5040Correct answer is option 'A'. Can you explain this answer?.

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