- #1

bodensee9

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I have a question about the number of ways to distribute a 6 hand card with at most 1 void in a suit (so you can have void in either spades, clubs, diamonds, heart, but you can't have a void in both spades and clubs, etc).

Would the solution just be the ways to distribute a 6 hand card (52 choose 6) - the ways to distriute cards with a void in 2 suits? (4 choose 2)*(26 choose 6)?

The reasoning is say the we have a universe of the total number of ways to distribute 6 cards, with no conditions. Included in that universe is the number of ways to distribute 6 hands with voids in 1 suit, and then included within that subset is the number of ways to distribute a 6 hand card with voids in 2 suits, etc. So to find the number of ways to distribute cards with either no void in any suite or with 1 void in a suite, wouldn't we just subtract out the number of ways to distribute cards with voids in 2 suits since that subset also includes the number of ways to distribute cards with voids in 3 suits?

Thanks.