Show proof of equality
Prove the following combinatorial relation: C(2n+2, n+1) = C(2n, n+1) + 2*C(2n, n) + C(2n, n-1). The proof must show proof of equality by left hand side and right hand side.
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In Las Vegas, there is simple game in which you put down $250 and are given exactly four cards from 52-card deck, one card at time. If you get the 2, 3, 4 and 5 card, in that order, you win $7,000 (the suit doesn't matter). How many possible four-
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