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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

Q1. 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?...

= {41*40*39*38*37*36*35!/ (35!*6*5*4*3*2*1)}
= 4496388 So, 4496388 number of 6-member committees can be selected from 41 members. Q2. From a standard 52-card deck, how many six-card hands consist...

Now, among rest of the 2 suits, one suit can be chosen in 2C1 ways and among
those 13 cards, 3 cards can be chosen in 13C; ways. So, the required set of cards as mentioned in the question can be...

Among the remaining two suits of cards, one suit of 13 cards can be chosen in 2C1
ways .............. (V) Among the chosen suit of 13 cards, 2 cards can be chosen in 13C2 ways. . ...(vi)
So, from...

There were people at the party Answer:—
Let the no. of people be 11.
It takes 2 persons to complete handshakes. So, if not a pair has repeated handshakes, then total no. of handshakes in the...

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