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[tex]\sum

Could someone give me a hint as to how to start this. I'm not sure how to really interpret it.

[tex](n-k)\binom{n}{k}=n\binom{n-1}{k}[/tex]

Right Side: Suppose you create a committe from [tex] \binom{n}{k} [/tex], then to pick a leader who isn't in the committee but in the pool of people, we have n-k ways.

Left Side: Suppose you have n ways to pick a leader for a group. After selecting the leader, you have n-1 people left to pick a committee of size k.

_{k=0}^{n}\binom{n}{k}^{2}=\binom{2n}{n}[/tex]Could someone give me a hint as to how to start this. I'm not sure how to really interpret it.

[tex](n-k)\binom{n}{k}=n\binom{n-1}{k}[/tex]

Right Side: Suppose you create a committe from [tex] \binom{n}{k} [/tex], then to pick a leader who isn't in the committee but in the pool of people, we have n-k ways.

Left Side: Suppose you have n ways to pick a leader for a group. After selecting the leader, you have n-1 people left to pick a committee of size k.

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