A research team requires 7 members, each one either a mathematician, computer sc
ID: 3238660 • Letter: A
Question
A research team requires 7 members, each one either a mathematician, computer scientist., or physicist. There are 8 mathematicians, 5 computer scientists, and 7 physicists in the pool of applicants for the team. How many possible teams are there (a) in total? (b) if there must be exactly 3 mathematicians on the team? (c) if there must be exactly 2 physicists and at least 2 computer scientists on the team? Suppose you choose any subset of 101 numbers from the set {1, 2, 3, ..., 200}. Show that one number in your subset must be a multiple of another number in your subset.Explanation / Answer
Solution:-
5)
a) Total number of possible teams is 77,520.
Total members required = 7
Number of mathematicians = 8
Number of Physicists = 5
Number of Computer scientists = 7
Total number of possible teams = 20C7 = 77,520
b) Total number of possible teams if exactly 3 mathematicians on the team is 27,720.
Total members required = 7
Number of mathematicians = 8
Other members = 12
Total number of possible teams if exactly 3 mathematicians on the team = 8C3 × 12C4 = 56 × 495 = 27,720
c) Total number of possible teams if exactly 2 physicsts on the team and atleast 2 computer scientists on the team is 60,060
Total members required = 7
Number of Physicists = 5
Number of Computer scientists = 7
Number of members those can be selected after 2 physicts and 2 computer scientists = 0 + 5 + 8 = 13
Total number of possible teams if exactly 2 physicsts on the team and atleast 2 computer scientists on the team = 5C2 × 7C2 × 13C3 = 10 × 21 × 286 = 60,060.
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