a group consists of 7 boys and 5 girls find the number of ways in which a team of 5 members can be selected so has to have atleast one boy and one girl
Answers
Answer:
"770 ways"
Step-by-step explanation:
There are 7 boys and 5 girls in a group
Total number of members = 7 + 5 = 12
If we want to select team of 5 members from group of 12 members in such a way that there is a girl and a boys at least present in a team
Strategy :
We use the combination to solve it
Let suppose we select the team in which all the girls then
Number of teams = ⁵C₅ = 5!/(5!×0!) = 1
If we select all the boys to make team of 5 members then
Number of teams = ⁷C₅ = 7!/(5!×2!) = 21
Now
If we select the team of 5 members from 12 members then
Number of teams = ¹²C₅= 12!/(5!×7!) = 792
Number of ways at least one girl & one boys = Total number - only boys - only girls
= 792 - 21 - 1
= 770
There are total 770 number of ways which fulfill the desire condition
Answer:
770
Step-by-step explanation:
a group consists of 7 boys and 5 girls find the number of ways in which a team of 5 members can be selected so has to have atleast one boy and one girl
Total members = 7 + 5 = 12
Total number of ways a team of 5 can be created
= ¹²C₅
= 12!/(5!7!)
= 792
If only boys are selected then ⁷C₅
= 7!/(5!2!)
= 21
If only girls are selected then ⁵C₅
= 5!/(5!0!)
= 1
Number of ways at least one girl & one boys = Total number - only boys - only girls
= 792 - 21 - 1
= 770
There are 770 number of ways in which a team of 5 members can be selected so has to have atleast one boy and one girl