DISCRETE MATHEMATICS SECTION 8.4 ARRANGEMENTS AND SELECTIONS WITH REPETITION

exercise #14 in how many ways can 10 identical quarters be distributed to 5 people?

1001

exercise #26 how many numbers greater than 50,000,000 can be formed by rearranging the digits in the number 13,979,397?

1050

exercise #24 how many positive integer solutions are there to the equation x+y+z=17?

120

exercise #4 how many 9 digit numbers can be formed by using the digits in the number 277,728,788?

1260

exercise #31 how many times is the PRINT statement executed? FOR I:=1 1 TO 10 FOR J:= 1 TO I FOR K:= 1 TO J PRINT I,J,K NEXT K NEXT J NEXT I

220

exercise #8 how many different boxes containing 10 wedges of cheese can be made by using wedges of cheddar,edam, gouda, and swiss cheese?

286

exercise #33 a pinochle deck consists of 2 of each of 24 different cards. how many different 12-card pinochle hands are possible?

287,134,346

exercise #20 twelve children are to be divided into groups of three to play three different games. In how many ways can the groups be chosen?

369600

exercise #18 in bridge a deal consists of distributing a 52-card deck into four 13-card hands. how many deals are possible in bridge?

52!/13!13!13!13!

exercise #29 how many positive integers less than 1,000,000 are such that the sum of their digits equals 12?

6062 (C(17,12)-6-30-30-60)

exercise #10 in how many different ways can 15 distinct books be distributed so that Carol receives 6, Don receives 4 and Eileen receives 5?

630630

exercise #32 A POUCH CONTAINS $1 IN PENNIES, $1 IN NICKELS AND $1 IN DIMES. in how many different ways can 12 coins be selected from this pouch?

88

exercise #28 how many distinct arrangements are there of two a's, one e, one i, one i, one o, and seven x's in which no two vowels are adjacent?

?

exercise #34 if m>/n. how many different ways are there to distribute m indistinguishable balls into n distinguishable urns with no urn left empty?

C(m − 1, m − n)+ C(m − 1, n − 1)