Question

Given a group of 10 men and 5 women:
a) how many ways can you choose a committee with 4 members
b) How many combinations of 4 have 2 men on them
c) have less men than women
d) if Mary and John won't serve together how many 4 members combinations are possible?

Answer 1

a)
\[C _{4}^{15}=1365\]

Answer 2

b)
\[C_{2}^{10}\times C _{2}^{5}=450\]

Answer 3

c)
\[C _{1}^{10}\times C _{3}^{5}=100\]

Answer 4

d)\[2\times C _{4}^{14}- C _{4}^{13}=1287\]