Question

How many 4-letter combinations containing 3 consonants and 1 vowel can be made from this set if all the letters in a combination must be unique? {R, E, L, O, A, D} A. 30 B. 48 C. 72 D. 90

Answer 1

Answer: C. 72

Explanation:

The set is:

{R, E, L, O, A, D}

if we separate it into consonants and vowels, we have

consonants: {R, L, D}

vowels : {E, O, A}

Now, we want combinations of 3 consonants and one vowel.

we have 4-letters combinations, let's fixate the first letter as the vowel,

for this first letter, we have 3 options {E, O, A}

for the second letter, a consonant, we also have 3 options {R, L, D}

for the third letter, we also need to choose a consonant, but now we have 2 options (because we already selected one)

for the fourth letter, we have only one option.

Now, the total number of combinations is equal to the product of the number of options in each selection:

C = 3*3*2*1 = 18

But remember that this is the case where the vowel is fixed for the first letter, we have 4 positions where the vowel can be (first, second, etc)

So the actual number of combinations is:

C*4 = 18*4 = 72

The correct option is C.