Question

1. Use the combinations formula to prove that in general C(n, r) = C(n, n - r).

2. Use the permutations formula to evaluate for any whole number n, P(n, 0). Explain the

   meaning of your result.

3. Use the combinations formula and the definition of 0! to evaluate, for

   any whole number n, C(n, 0). Explain the meaning of your result.

4. Suppose you have 35 songs for a playlist consisting of only 5 songs. How many different playlists can you have?

Answer 1

C(n, 0) in the definition of combination operator is defined as the number of ways to select no item from n items that is 1.

Therefore, C(n ,0) = 1

Therefore 0! = 1 here.

b) Assuming that the songs order is important, the number of playlists of 5 songs from the 35 songs is computed as the number of permutations of 35 songs taken 5 at a time

= 35*34*33*32*31

= 38955840

Therefore 38955840 is the required number of different playlists possible here.