using the letter in ADJUSTING without repeats. a. how many of these nine-arrangements have a consonant in fifth position and J in the sixth position? b. if a nine-letter arrangement is selected at

Question

using the letter in ADJUSTING without repeats.

a. how many of these nine-arrangements have a consonant in fifth position and J in the sixth position?

b. if a nine-letter arrangement is selected at random, what is the probability that a consonant is fifth and J is sixth?

Answer 1

a) 5*7!

There's no choice for the 6th position- must put J there.

Other than J, the consonants in ADJUSTING are D, S, T, N and G. The important thing is that there are 5 of them, so there are 5 choices of consonant to put in the 5th position.

There are 7! ways to populate the 7 remaining slots (7 choices for the letter that goes in the 1st position, leaving 6 choices for 2nd position and so on).

b) There are 9! nine-letter arrangements. We'll regard them all as having equal probability.

P(consonant in place 5 & J in place 6) = 5*7!/9! = 5/(8*9) = 5/72