Solve the following problems and show all work! a. How many 5-card poker hands e

Question

Solve the following problems and show all work!

a. How many 5-card poker hands either contain a straight (5 consecutive cards) or a flush (5 cards of the same suit)?

b. There are 5 men in a theater company, and that theater company puts on 7 plays. Each of those men appears in exactly 3 of the plays. Prove that one of the plays must have at least 3 of the men in it.

c. How many natural number solutions are there to x + y + z ? 50, given that x, y, and z all must be at least 3?

d. How many 8-letter passwords are there that are not palindromes?

f. On a 7 by 7 chessboard, you have a pawn on each square. Is it possible to simultaneously take each pawn and move each of them to an (horizontally or vertically) adjacent square, so that each square ends up with one pawn on it again? For example, on a 2x2 chessboard it would be possible, because you could move each pawn one space clockwise and each square would get one pawn again. (Hint: the colors of the squares will help you)

g. How many ways are there to distribute 50 gold coins among 6 pirates, if one of them is the captain and must receive at least 20 coins, and none of the other 5 pirates can receive 20 or more coins?

h. How many 9-letter passwords are there that contain exactly 4 X’s, exactly 4 Y’s, or exactly 4 Z’s?

Explanation / Answer

Solution:

1)Answer:

->fivecardswithconsecutivevalues 5432A --->flush:fivecardsofthesamesuit

K9763

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.