Question

From a group of 8 men and 8 women 8 members are to be selected for a team such that women constitut at least 50 % of the team in how many ways can be done

Answer 1

4 men. 4womeen are selected for a team

Answer 2

Solution:

Total members in the team = 8 men + 8 women= 16 members

→We have to select 8 members  out of 16 members in such a way that women constitute 50% i.e atleast 4 women should be in team.

This can be done in following ways: → $_{4}^{8}\textrm{C}\times_{4}^{8}\textrm{C}+_{3}^{8}\textrm{C}\times_{5}^{8}\textrm{C}+_{2}^{8}\textrm{C}\times_{6}^{8}\textrm{C}+_{1}^{8}\textrm{C}\times_{7}^{8}\textrm{C}+_{0}^{8}\textrm{C}\times_{8}^{8}\textrm{C}$

=70² + 56²+28²+8²+1

= 4900+3120+784+64+1

= 8869 ways