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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

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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?...

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= {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...

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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...

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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...

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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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