Solutions Manual to Accompany Combinatorial Reasoning by DeTemple Duane; Webb William; & William Webb

Author:DeTemple, Duane; Webb, William; & William Webb [Detemple, Duane & Webb, William]
Language: eng
Format: epub
ISBN: 9781118830826
Publisher: John Wiley & Sons, Incorporated
Published: 2014-08-19T00:00:00+00:00

4.3.11.

Use PIE to calculate the number of ways that a 5-card hand can be dealt from a 52-card deck with at least one card of every suit.

Check your answer to part (a) by using a more direct approach.

Answer

Let the suits be numbered 1, 2, 3, and 4, and let Ai be the 5-card combinations missing suit i. Thus

Using PIE, there are hands with no suit missing.

Choose which suit has two cards, and then the ways cards can be chosen from the four suits: = 685,464.

4.3.13.

Use PIE to show there are six solutions in integers of the equation t1 + t2 + t3 = 16, where 2 ⩽ t1 ⩽ 6, −1 ⩽ t2 ⩽ 4, and 0 ⩽ t3 ⩽ 8.

List the six solutions.

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