Question

How many combinations are possible while selecting four letters from the word SMOKEJACK with the condition that S must appear in it?

a) 1
b) 10
c) 11
d) 8

Answer 1

To find the number of combinations to select four letters from the word SMOKEJACK, with S included, calculate the combinations of the remaining three letters from the nine distinct letters left. The formula is C(9, 3) = 84 different combinations.

Step-by-step explanation:

The question asks for combinations which involve selecting four letters from the word SMOKEJACK, with the condition that the letter S must appear in the combination. Since S must be included, we only need to choose the remaining three letters from the remaining nine distinct letters (M, O, K, E, J, A, C).

The number of ways to choose three letters from these nine is given by the formula for combinations, which is C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial. Here, n is 9 and k is 3. Therefore, the number of combinations is C(9, 3) = 9! / (3!(9-3)!) = 84.

Thus, considering that S will always be one of the four letters, we have 84 different combinations when selecting the other three letters.