1 a password of length 7 is to be generated which contains o

1) a password of length 7 is to be generated which contains only two of the letters from a-z , one letter repeated 3 times and the other letter repeated 4 times. how many such passwords are there?

2)Suppose that 10 children are to be lined up. a) In how many ways can this to be done? b) if 5 of the children are girls and 5 are boys, in how many ways can they be lined up so that the girls are grouped toghther and the boys are grouped together? c) if 10 children are lined up at random, what is the probability that the girls are grouped togther and the boys are grouped together?

3) Suppose that you are delt a 5 card poker hand. what is the probability that ou are dealt a full house, that is, 3 cards of one rank and two cards of another rank?

Solution

1) Ways to choose 3 places out of 7 = 7C3 , the number of ways to select a letter = 26

7C3 * 26

Then remaining 4 places can be filled with 4C4 * 25 ways

Total ways= 7C3 * 26 * 4C4 * 25 = 22750

2) a. 10! = 3628800

b. 2 * 5! * 5! = 28800

c. P= 28800/3628800 = 0.007937

3) 13 * 4C3 * 12 *4C2

= 3744