1. There are 6 women and 5 men applying for positions at Walmart in Toronto. There are only 4 positions available.

Question

1. There are 6 women and 5 men applying for positions at Walmart in 

   Toronto. There are only 4 positions available. 

a) In how many ways can these four (4) positions be filled?

b) In how many ways can these 4 positions be filled if all the women are hired?

c) In how many ways can these 4 positions be filled if 2 men and 2 women are hired?

d) In how many ways can these 4 positions be filled if at least 1 man is hired.

Answer 1

a) 11 choose 4 = 11!/(7!*4!) = 11*9*8/(4*3*2*1) = 11*3 = 33

b) if only women are hired the answer is 6 choose 4 = 6!/(4!*2!) = 6*5/2 = 15

c) 6 choose 2 plus 5 choose 2 = 6!/(4!*2!) + 5!/(3!*2!) = 6*5/2 + 5*4/2 = 15+10 = 25

d) the answer of part a minus the answer of part b = 33 - 15 = 18