In how many ways can a pack of 52 cards be (i) divided equally among four players in order (ii) divided into four groups of 13 cards each (iii) divided in 4 sets, three of them having 17 cards each and the fourth just one card?

Question

DivineJEE · Accepted Answer

(i) The number of ways in which 52 cards be divided equally among four players in order = ^52 C_13 x ^39 C_13 x ^26 C_13 x ^13 C_13=frac52(13)^4 (ii) The number of ways in which a pack of 52 cards can be divide equally into four groups of 13 cards each (1 / [4) ^52 C_13 x ^39 C_13 x ^26 C_13 x ^13 C_13=(52 / [4(13)^4.) (iii) The number of ways in which a pack of 52 cards be divided into four sets, three of them having 17 cards each and fourth just one card =(1 / [3) x ^52 C_17 x ^35 C_17 x ^18 C_17 x ^1 C_1=frac523(17)^3

Explanation

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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