4. A group of 10 engineers is composed of & mechanicals a a) (7 marks) in how ma

Question

4. A group of 10 engineers is composed of & mechanicals a a) (7 marks) in how many ways can S out 10 e Spring 2018) and 4 electrical. project? t of any 10 engineers be chosen to work on a particular marks) Suppose that the chosen 5 engineers must be comprised of 3 mechanicals and 2 electricals. Now in how many ways can the group of b) (7 5 be chosen? c) (6 marks) The 6 mechanicals are also competing for two different awards, onef performance and the other for innovation. If each can receive at most one of th awards, in how many ways can these two awards be allocated to the 6 mecha

Explanation / Answer

a) Number of ways in which 5 can be chosen from 10 = 10C5

= 10! /(5! X 5!)

= 252

b) In this case, number of ways in which 5 can be chosen = 6C3 x 4C2

= 6!/(3!x3!) X 4!/(2!x2!)

= 20 x 6

= 120

c) number of ways in which awards can be allocated = 6P2 = 6X5 = 30

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