Question

Consider a group of 5 females and 7 males. The number of different teams consisting of 2 females and 3 males, that can be formed from this group, if there are two specific males A and B, who refuse to be the member of the same team, is​

Answer 1

Step-by-step explanation:

Given Consider a group of 5 females and 7 males. The number of different teams consisting of 2 females and 3 males, that can be formed from this group, if there are two specific males A and B, who refuse to be the member of the same team, is

• So total will be 5 C 2 x 7 C 3
•                   = 5! / 2! 3! x 7! /  3! x 4!
•                 = 10 x 35
•                = 350
• Now remaining males will be 7 – 2 = 5
• Both males in the same team will be 5 C 2 x 5 C 1
•                                                    = 10 x 5  
•                                                    = 50
• So required total – both males will be  
•                                         = 350 – 50

                                       = 300

Answer 2

Given:  a group of 5 females and 7 males

To find: no. of teams that can be formed if two males A and B  refuse to be the member of same team.

Solution:

• Now, the total teams that can be formed will be:

      =  5 C 2 x 7 C 3 

      =  5! / (2! X 3! ) x  7! /  (3! X 4!)

      =  10 X 35

      =  350

• So the remaining males that will not be a part of same team are:

       7 – 2 = 5

• Now, both males in the same team, will be:

       5 C 1 X 5 C 2

       = 5 X 10

       = 50

•  So the total number of teams that can be formed by 2 females and 3 males, if there are two specific males A and B, who refuse to be the member of the same team are:

       = 350 – 50

       = 300

Answer:

            So total teams that can be formed are 300.