Statistics 50 Exercises

1.       How many 4 digit numbers can be formed from the digits 1, 3, 5, 7, and 8 if none of these appears more than once in each number?

2.       A girl has invited 5 friends to a dinner party.  After locating herself at the table how many different seating arrangements are possible?

3.       From 7 men and 4 women, how many committees can be selected consisting of:

(a)     3 men and 2 women

(b)    5 people of which at least 3 are men

4.       How many committees consisting of 3 representatives and 5 senators can be selected from a group of 5 representatives and 8 senators?

5.       In how many seating arrangements can 8 men be placed in a row of chairs if there are 3 who insist on sitting together?  Consider two seating arrangements different unless each man sits in the same chair in the two arrangements.

6.       A certain college has only 3-unit courses in 13 of which a freshman may enroll.  Find the number of 15-unit programs a freshman can consider if:

(a)     there are no specific requirements

(b)    English 1 and History 1 are required courses

7.       There are 10 chairs in a row

(a)     In how many ways can 2 people be seated?

(b)    In how many of these ways will the 2 people be sitting alongside one another?

(c)     In how many ways will they have at least 1 chair between them?

8.       A railway coach has 12 seats facing backward and 12 facing forward.  In how many ways can 10 passengers be seated if 2 of these people are known to refuse to ride facing forward and 4 refuse to ride facing backward?

9.       Five red books and 3 green books are placed at random on a shelf.  Find the probability that the green books will all be together.

10.    Six married couples are standing in a room. If 2 people are chosen at random, find the probability that:

(a)     they are married to each other

(b)    one is male and the other is female