Finite Math. Really need to know how to do these questions.

Question

1. How many distinct 9-letter words starting with “i” can be formed from the word “committee”?
2. How many distinct 4-letter words can be formed from the word “books”

Answer 1

Mesa,

1.

Let's put the letter "i" down to the first spot, so we have 8 more spots to fill out with the letters: 1c, 1o, 2m, 2t, and 2e. This is permutation with repetitions, so the answer is 8!/(2!2!2!) = 5040.

Another way to thin about is that you choose 1 spot for a "c" : C(8,1), then 7 spot remains

Then you choose one spot for "o": C(7,1), then the 2 m's: C(6,2), the 2 t's: C(4,2) and the e's: C(2,2)

This gives you C(8,1)*C(7,1)*C(6,2)*C(4,2) *C(2,2) = 5040 different ways

2.

We have 2 options, whether we choose the 2 o's or not. If we do:

Let's find 2 spots for the 2 o': C(4,2) ways, the next spot we have 3 choices( b, k or s): C(3,1), and for the last spot 2 choices left: C(2,1)

If we don't have 2 o's: we have 4*3*2*1 choices (4 choices for the first spot, 3 for the next etc.

We have to add the 2 options:

C(4,2)*C(3,1)*C(2,1) + 4*3*2*1 =36 + 24 =60 different ways.

Let me know if you have more questions.