In how many ways can a group consisting of 5 girls and 4 boys be formed from a class of 8 girls and 5 boys
Answers
Given,
4 boys are chosen from a total of 5 boys
5 girl`s are chosen from a total of 8 girl`s
To Find,
Total ways of choosing group =?
Solution,
The number of ways of choosing 4 boys from 5 boys = 5C4
The number of ways of choosing 4 boys from 5 boys = 5!/(1!*4!)
The number of ways of choosing 4 boys from 5 boys = 5 ways
The number of ways of choosing 5 girl`s from 8 girl`s = 8C5
The number of ways of choosing 5 girl`s from 8 girl`s = 8!/(5!*3!)
The number of ways of choosing 5 girl`s from 8 girl`s = (8*7*6) / (3 * 2)
The number of ways of choosing 5 girl`s from 8 girl`s = 56 ways
Total ways of choosing group = 56 * 5
Total ways of choosing group = 280 ways
Hence, in 280 ways a group consisting of 5 girl`s and 4 boys be formed from a class of 8 girl`s and 5 boys.