Seven movies (A, B, C, D, E, F, and G) are being scheduled for showing. The order of showing is determined by random selection. Find the probability that film C will be shown first, film A next-to-last, and film E last. Solution total number of ways 7 slots can be filled randomly by seven movies= 7!=5040 required arrangement is 1st slot for C, 6th slot for A ,7th slot for E and balance 4 slots are to be randomly filled by B,D,F and G number of ways 4 slots can be filled randomly by 4 movies= 4!=24 pro. of filling the 7 slots as per the question = 24/5040=1/210.

1. Seven people are preparing to play basketball using a five member team. How many different
five person teams can be put together. Hint: Combination of 7 taking 5 at a time.
Solution
from seven member, selecting a five member team.
means that we have to reject two member out of seven member to form a team.
Selecting 2 (otherway around)out of sevel,
Nos of way = nCr = 7C2 = 7*6/2 = 21 ways