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EECS 210 Quiz 5 Answers 1. (2) How many distinct arrangements are there of the letters in the word RECURRENCE? 10!/(3!•2!•3!) 2. (2) There are three identical boxes one with white, one with red and one with blue marbles. Each box has at least 18 marbles. In how many ways can 18 marbles be selected if there are no restrictions C(18 + 3 – 1, 18) = C(20, 18) 3. (3) What is the coefficient of the x9y11 term in the expansion of (x + 2y)20? C(20, 11)•211 4. (2) How many different five card hands contain at least one card from each suit? 4•C(13, 2)•[C(13, 1)]3 5. A wedding party with seven people is being photographed. In how many ways can the members of the wedding party be arranged in a line if a. (3) the bride must be next to the groom? 2•6! b. (3) the bride is to the left of the groom? 1 + 2 + 3 + 4 + 5 + 6 = 21 ways to place the bride and groom and 5! ways to arrange the rest of the people so the answer is 21•5! 6. Consider 5-digit numbers a. (3) How many contain exactly two 4’s? 4•93 Choose spot for 2nd 4, then fill the rest + 4 not in 1st position C(4, 2)•8•92 choose spots for the 4’s 8 ways for first digit, 92 for the rest 4 in 1st position b. (3) How many without 0’s contain exactly four distinct digits? (i.e. two digits are the same). 9•C(5, 2)•8•7•6 Choose the digit to have two of, choose the places for that digit, fill in the remaining three digits EECS 210 Quiz 5 Answers 1. (2) How many distinct arrangements are there of the letters in the word REOCCURRENCE? 12!/(3!•3!•3!) 2. (2) There are three identical boxes one with white, one with red and one with blue marbles. Each box has at least 15 marbles. In how many ways can 15 marbles be selected if there are no restrictions C(15 + 3 – 1, 15) = C(17, 15) 3. (2) What is the coefficient of the x8y12 term in the expansion of (2x + y)20? C(20, 12)•28 4. (2) How many different five card hands contain at least one card from each suit? 4•C(13, 2)•[C(13, 1)]3 5. A wedding party with eight people is being photographed. In how many ways can the members of the wedding party be arranged in a line if a. (3) the bride must be next to the groom? 2•7! b. (3) the bride is to the left of the groom? 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 ways to place the bride and groom and 6! ways to arrange the others so the answer is 28•6! 6. Consider six-digit numbers a. (3) How many contain exactly two 4’s? 5•94 Choose spot for 2nd 4, then fill the rest + 4 not in 1st position C(5, 2)•8•93 choose spots for the 4’s, 8 ways for first digit 93 for the rest 4 in 1st position b. (3) How many without 0’s contain exactly five distinct digits? (i.e. two digits are the same). 9•C(6, 2)•8•7•6•5 Choose the digit to have two of, choose the places for that digit, fill in the remaining four digits