In how many ways can you choose 5 people out of 9 people to form a 5-member comm
ID: 3170599 • Letter: I
Question
In how many ways can you choose 5 people out of 9 people to form a 5-member committee? b) In how many different orders can 8 people line up in a gas station that has a single gas pump? c) In how many different orders can n people line up in a gas station of two parallel gas pumps? d) In how many different orders can 10 runners finish a race if 3 people tie for the first place, 2 people tie for second place, 2 people tie for the third place, and no ties otherwise? e) A coin is tossed 10 times. Each outcome is a sequence of 10 heads and/or tails. What is the number of possible outcomes where the number of heads is exactly 4? At least 4? At most 4? f) Suppose that in a state, all car license plates consist of 6 characters where each character can be a capital letter or a decimal digit. i. How many different license plates are possible? ii. How many possible plates where the first two characters are letters, and the last two characters are digits? iii. How many plates that have just 3 letters are possible? g) A diet is thrown 10 times, where the die has 6 faces labeled 1, 2, ..., 6. Each outcome will be a sequence of 10 faces (i.e., 10 digits), where each face is one of the 6 values. i. What is the number of possible outcomes where face 2 comes up exactly 3 times? ii. What is the number of possible outcomes where face 2 comes up exactly 2 times and face 3 comes up exactly 3 times? h) One urn contains 20 balls: 5 balls are red (labeled R_1, R_2, ..., R_5), 6 are blue (labeled B_1, B_2, ..., B_6), and 9 are white (labeled W_1, W2, ..., W_9). You draw 8 balls from the um. What is the number of possible outcomes where 2 of the drawn balls are red, 3 are blue, and 3 are white?Explanation / Answer
(A)
Selection of 5 member committee from a group of 9 can be done in 9C5 ways i.e. 126
(B)
Arraning 8 people in different orders can be done in 8! = 40320 ways
(C)
n number of people can be divided into two groups in (n+2-1)C(2-1) ways i.e. (n+1) ways
Number of ways n people can be arranged for two gas station (n+1)*n! ways
(D)
possible number of orders are - 10C3 * 7C2 * 5C2 * 3!