Question

In how many ways a team of 11 must be selected from 5 men and11 women such that the team comprises of not more than three men?a.1234b. 1565

c. 2456d. 2256

Answer 1

Let S be Sample space
and E be event of selecting a team of 11 members from 5 men and 11 women such that team consists of not more than 3 men

Total members=16

n(S)= Selecting 11 members from 16
= 16C11
= 4368

Possible cases =>
a) 1 men + 10 women
No. of ways of selecting= 5C1 + 11C10
= 5C1 + 11C1
= 5+11
= 16.

b) 2 men + 9 women
No. of ways of selecting= 5C2 + 11C9
= 5C2 + 11C2
= [(5*4)/2 + (11*10)/2]
= (20+110)/2= 130/2
= 65

c) 3 men + 8 women
No. of ways of selecting= 5C3 + 11C8
= 5C3 + 11C3
= [(5*4*3)/(3*2) + (11*10*9)/(3*2)]
= (60+990)/6
= 1050/6
= 175


n(E) = 16 + 65 + 175
n(E) = 256


Required probability =n(E)/n(S)
=256/4386
=128/2193

hope it helps
;)