In how many ways can 3 consonants and 2 vowels be selected from the letters of the word TRIANGLE?
Answer: 30
Explanation
Identify the consonants and vowels in the word TRIANGLE:
Consonants: T, R, N, G, L
Vowels: I, A, E
We need to select 3 consonants from the 5 consonants:
Number of ways to select 3 consonants = 5C3 = 5! / (3! x 2!) = 10
We need to select 2 vowels from the 3 vowels:
Number of ways to select 2 vowels = 3C2 = 3! / (2! x 1!) = 3
Now, we need to find the total number of ways to select 3 consonants and 2 vowels:
Total number of ways = Number of ways to select 3 consonants x Number of ways to select 2 vowels
= 10 x 3
= 30
So, the correct answer is:
30
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