Question

# 1.How many different committees can be formed from

7 teachers and 34 students if the committee consists of 4 teachers and 2

students?

In how many ways can the committee of 6 members be selected?

2.From a standard 52-card deck, how many six-card hands consist of one king, two cards

of another denomination, and three cards of a third denomination?

The number of possible hands is ___

3.From a standard 52-card deck, how many eight-card hands consist of three cards of one denomination, three cards of another denomination, and two

cards of a third denomination?

The number of possible hands is___

4 If a "word" is interpreted to be a sequence of letters, how many six-letter words with no repeated letters contain three

vowels? (Note that y is not considered a vowel.)

There are ___ words

5 At a party, 171 handshakes took place. Each person shook hands exactly once with each of the others present. How many people were at the party

There were ___people at the party