There are n boys and m girls.A group of p people should be formed where there should be min 4 boys and 1 girl.Find total number of way of forming the group if number of boys n is 5,number of girls m=2 and total number of people p is 5.How to go about solving this problem
Calculate number of ways .Combination problem
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combinatorics
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0Well, we don't need to **use** the symbol $\binom{n}{k}$. The $4$ boys can be chosen in $5$ ways (there are clearly $5$ ways to choose who *won't* be on the committee). And then there are $2$ ways to choose the girl. At a more basic level, we can *list* all the committees and count. Give the boys and girls names. Simplest way to list the committees is as $(X,Y)$, where $X$ is the boy who is left out, and $Y$ is the girl who is left out. – 2012-02-09
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There are $5$ boys and $2$ girls and you want to form a group of $5$ with at least $4$ boys and $1$ girl. That means you should choose $1$ girl and $4$ boys. This can be done in $\binom 21\times \binom 54=10$ ways.