In boys many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Created: 3 months ago |
Updated: 3 weeks ago
To find the number of ways to choose a group of 5 men and 2 women from a total of 7 men and 3 women, you can use combinations.
The number of ways to choose 5 men out of 7 is given by (57), and the number of ways to choose 2 women out of 3 is given by (23).
So, the total number of ways to choose the group is the product of these two combinations:
(57)×(23)
Using the formula for combinations, where (rn)=r!(n−r)!n!, we can calculate:
(57)=5!(7−5)!7!=5!2!7!=2×17×6=21
(23)=2!(3−2)!3!=2!1!3!=23=3
So, the total number of ways is:
21×3=63
Therefore, there are 63 ways to form a group consisting of 5 men and 2 women from a total of 7 men and 3 women.
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