1) Solve for the factorials below: Show Show Answer 24 b) 0! Show Answer 1 c) (3!)(2!) Show Answer 12 d) 10!/8! Show Answer 90 2) Evaluate each: Show Answer 9!=362,280 b) 9C9 Show Answer 1 c) 9P5 Show Answer 15,120 d) 9C5 Show Answer 126 Be careful, I mixed in some problems that are not Permutation/Combination into the below set.3) How many ways can you turn in a batting order for a baseball team if you only have 9 players? Show Answer 9P9=362,280 4) Suppose a lawyer must select 4 jurors from a set of six candidates? How many groups are possible? Show Answer 6C4=60 5) How many ways can 3 runners be selected for the Olympics from a field of 5 contestants? Show Answer 5C3=10 6) How many ways can the first 3 places be awarded in a race involving 5 contestants (excluding ties)? Show Answer 5P3=60 7) How many ways can the positions of president and vice president be assigned from a group of 8 people? Show Answer 8P2=56 8) Find the Number of hugs possible in a family of 5 people (no repeat hugs). Show Answer 5C2=10 9) You have 9 families you would like to invite to a wedding. Unfortunately, you can only invite 6 families. How many different sets of invitations could you write? Show Answer 9C6=84 10) Suppose we have to select 5 managers from a list of 10. How many ways can this be done? Give the correct expression that gives the answer. Show Answer 10C5 11) Suppose we have to select a manager, assistant manager, and night manager from a list of 10 people. How many ways can this be done? Give the correct expression that gives the answer. Show Answer 10P3 12) How many ways can a 3-card hand be selected from a standard 52-card deck? Give the correct expression that gives the answer. Show Answer 52C3 13) Three cards are selected randomly and given to 3 players. How many possibilities exist? Give the correct expression that gives the answer. Show Answer 52P3 14) A card is select from a standard deck of cards, then put back and the deck is shuffled. This is done 3 times. How many 3-card hands can you receive? Show Answer 52*52*52=140,608 15) At a Fiat dealership a total of 3 cars of a particular model must be transported to another dealership. If there are 25 cars of this type, how many choices are available for transport? Show Answer 25C3=2300 16) At a Fiat dealership a total of 3 cars of a particular model must be transported to another dealership. If there are 25 cars of this type, how many ways can they be loaded onto the truck for transport? Show Answer 25P3=13,800 17) At a Fiat dealership there are 25 cars of a certain model.
Fifteen have automatic transmission. Twelve have leather seats. Ten cars have both automatic transmission and leather seats. Show Answer 17 b) How many have neither automatic transmission nor leather seats. Show Answer 8 18) Social Security numbers consist of 9 digits (0-9). If there are no restrictions, how many different social security numbers are possible? Show Answer 10*10*10*10*10*10*10*10*10=109 =1,000,000,000 19) Suppose license plates in one state have 4 letters followed by 2 digits. Show Answer (264)(102)=45,687,600 b) What if only letters cannot be repeated? Show Answer 26(25)(24)(23)(102)=35,880,000 c) What if only digits cannot be repeated? Show Answer (264)(10)(9)= 41,127,840 20) A shipment of 20 disk drives were received by a computer store. Four of the drives are defective. A sample of 2 are selected randomly. Show Answer Combination Problem: 20C2=190 b) How many of the samples contain 2 defective drives? Show Answer Combination Problem: 4C2=6 c) Suppose one of the samples is tested and one sample is sold. How many ways can this be done? Show Answer Permutation Problem: 20P2=380 21) Suppose a 5-card hand is selected from a standard deck of cards. How many ways can the following be done? Show Answer (4C3)(4C2)=4(6)=24 b) Select exactly 3 fours. Show Answer (4C3)(48C2)=4(1128)=4512 c) At least 4 hearts Show Answer 27885+1287=29,172 22) Suppose we have an office of 5 women and 6 men and need to select a 4 person committee. How many ways can we select Show Answer (5C2)(6C2)=150 b) 3 men and 1 woman? Show Answer (5C3)(6C1)=60 c) All women? Show Answer (5C0)(6C4)=15 or just 6C4=15 23) . A lottery consists of 54 numbers. To purchase a ticket, you select 6 numbers from 54 without repetition. How many selections are possible? (In lotteries, the order is generally not relevant.) Show Answer 54C6=25,827,165 Just for fun, what if you had to get the numbers in the order selected? Show Answer 54P6=18,595,558,800 (don't hold your breath) 24) Out of 30 applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female graduates, 2 are bilingual women, 6 are bilingual graduates and 2 are bilingual female graduates. Find the number of female graduates that are not bilingual. Show Answer 1 25) a) How many 3 letter code words can be selected if there are no restrictions? b) How many 3 letter code words can be selected if repetition is not allowed? Answer a) 17,576 Answer b) 15,600 26) Seven coins are tossed. How many different ways can they land? Show Answer 27 =128 27) Show Answer 350 b) a group of 2 women and 3 men? Show Answer 210 c) a group of all women? Show Answer 21 d) a group of all men? Show Answer 1 What does 10p5 mean Quizizz?116280. 120 seconds. Q. What does 10P5 mean? Permutations with 5 choices and 10 positions.
How many ways can his coach choose five starting players?How many different possible ways can the coach choose a team of 5 players? 12C5 = 792 ways the coach can choose a team of 5.
How many identification code are possible by using 3 letters if no letter may be repeated?Thus there are 15,600 identification codes.
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