Question

If the permutation of the word WHITE is selected at random, how many of the permutations Begins with a consonant

Answer 1

Answer: 72

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Step-by-step explanation:

If W is the first letter, then we have 4 ways to select the other letters. The order matters so we use a permutation. Use either the nPr formula or the factorial notatation.

nPr = 4P4 = (4!)/(4-4)! = 24/1 = 24

or simply 4! = 4*3*2*1 = 24

We have 24 ways to pick the four other letters after W is chosen.

This logic applies if H is the first letter or if T is the first letter. Imagine 3 rows of 24 different cells per row. Each row represents the first letter (W, H or T). In total, we have 3*24 = 72 cells overall.

You can write the complete steps as 3*4! = 3*24 = 72.