Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2...
Ans : 25200soln :Number of ways of selecting words (3 consonants out of 7) and (2 vowels out of 4) = (7C3×4C2) = 210.
Number of groups, each having 3 consonants and 2 vowels = 210.Each group have 5 letters.
Number of ways of arranging 5 letters among themselves = 5! = 120
Formed number of ways = (210 x 120) = 25200...
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2...
To solve this problem, we can use the concept of combinations.
Combination is a way to select items from a larger set without considering the order in which they are selected. In this case, we want to select 3 consonants out of 7 and 2 vowels out of 4.
Let's solve this step by step:
Step 1: Selecting 3 consonants out of 7
To find the number of ways to select 3 consonants out of 7, we can use the formula for combinations:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
Using this formula, we can calculate the number of ways to select 3 consonants out of 7:
C(7, 3) = 7! / (3!(7-3)!)
= 7! / (3!4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
So, there are 35 ways to select 3 consonants out of 7.
Step 2: Selecting 2 vowels out of 4
Similarly, we can find the number of ways to select 2 vowels out of 4:
C(4, 2) = 4! / (2!(4-2)!)
= 4! / (2!2!)
= (4 * 3) / (2 * 1)
= 6
So, there are 6 ways to select 2 vowels out of 4.
Step 3: Finding the total number of words
Now, we need to find the total number of words that can be formed using the selected consonants and vowels. Since the order of the consonants and vowels matters, we need to multiply the number of ways to select consonants by the number of ways to select vowels.
Total number of words = Number of ways to select consonants * Number of ways to select vowels
= 35 * 6
= 210
Therefore, the correct answer is option A) 210.