Probability Worksheet 4. Simplify the expressions. n n 10! 2!8! 1.) 2.) 3.) ) 7! 5! 5! 5.) 4.) 14 7.) 8.) 2 2 n!

Transcription

1 M408 Probability Worksheet 4 Name Simplify the expressions. 1.) 10! 2!8! 2.) n n ) 5 P 2 4.) 14 C 9 5.) ) 3! 7! 5! 5! 7.) x 3 4 n 3! x 2 4 n 1! 8.) x n! x 4 2 2n 2! 9.) Find the value of n in the equation 42 P n,3 P n,5. 10.) Is P n, n 1 less than, greater than, or equal to P n, n? Show work.

2 11.) How many different ways can six people line up in a straight line? 12.) The Greek alphabet consists of 24 letters. How many Greek fraternity names can be formed, each containing either 2 or 3 letters with repetition allowed? 13.) An inspector from the health department arrives at Fremd to check for possible food contamination. There are 20 portion of food prepared. The inspector decides to test 8 of these portions. In how many different ways can 8 portions be selected? 14.) Don has 5 pennies, 3 nickels, and 4 dimes. How many can they be arranged in a row? 15.) A bag contains 4 red, 6 white, and 9 blue marbles. How many ways can 5 marbles be chosen to meet the following conditions? a) all marble are white b) all marbles are blue c) at least two marbles must be blue d) 2 are red, 2 are white and 1 is blue e) 2 are one color and 3 are another color

3 16.) How many different positive integers, with no two digits in any integer alike, and with no integer having an initial digit of 0, can be formed with digits chosen from the set {0,1,2,3,4}? 17.) 3 algebra books and 7 geometry books, all different, are placed on a shelf. If all the algebra books are kept together, in how many ways can all the math books be arranged? 18.) There are 8 seats in the King s station wagon. In how many ways can Mr. and Mrs. King and their 6 children be seated if only the parents drive? 19.) To deal with the budget problems in district 211, the principal would like to form a committee of 7 people to discuss budget cuts. The group consists of 2 students, 4 teachers, and 1 administrator. If 23 teachers, 15 students, and 5 administrators volunteered, in how many ways can the committee be formed? 20.) In a certain state, each automobile license plate number consists of two letters followed by a four digit number. To avoid confusion between O and zero and I and one, the letters O and I are not used. How many distinct license plate numbers can be formed? Repetition is allowed.

4 21.) If a customer purchases a new stereo system during the spring sale, he may choose any 6 CDs from 20 classical and 30 jazz selections. In how many ways can the customer choose 3 of each? 22.) King Arthur and his eight knights sit down at the Round Table. One of the knights is Sir Lancelot. How many ways can King Arthur seat himself and the eight knights if Lancelot sits directly to the left of King Arthur? 23.) A teacher wants to write a 5 question test from a pool of 8 questions. How many ways can the teacher write the test? 24.) How many 13-card hands are there having exactly 6 spades, 4 hearts, 1 diamond, and 2 clubs from a deck of 52 cards? 25.) Three people are lining up for a ride on a toboggan, but only two of the three people want to take the first position. With that constraint, in how many ways can the three people be seated on the toboggan?

5 26.) License plates are made using five of the following digits 1,2,3,4,5,6,7. How many plates are possible if an odd digit must come first and a) repetitions are allowed? b) repetitions are not allowed? 27.) From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many different ways can the offices be filled? 28.) From a pool of 12 candidates, a committee of four people is made. In how many different ways can the committee be formed? 29.) A combination lock will open when the right choice of three numbers (from 1 to 40, inclusive) is selected. How many different lock combinations are possible? 30.) You draw 5 cards from a deck of 52 cards. How many 5-cards hands are there having with four cards from the same suit? (That is, four cards are from one suit and one card is from another suit.)

6 31.) Find how many different ways the letters of the word STATISTICS can be arranged. 32.) How many different ways can all the letters of the word MASSACHUSETTS be arranged? 33.) There are 3 identical red flags and 5 identical white flags. If all flags are to be used how many signals can be given? 34.) How many ways can you arrange five keys on a key ring? 35.) Find the number of ways to arrange five keys on a ring with a clasp. 36.) How many ways can you arrange 7 people at a round table? 37.) How many ways can you arrange 7 people at a table with a special seat for the head of the table?