Classical

Combinatories - Combinatories MCQ

11:  

 In how many ways can 5 red and 4 white balls be drawn from a hag containing 10 red and 8 white balls ?

A.

8C5 x 10C4

B.

10C5 x 8C4

C.

18C9

D.

None of these

 
 

Option: B

Explanation :

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12:  

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

A.

3600

B.

120

C.

7200

D.

None of these

 
 

Option: A

Explanation :

3 consonants out of 5 can be selected in 5C3 ways.
2 vowels out of 4 can be selected in 4C2 ways.
Therefore, total number of groups each containing 3 consonants and 2 vowels =  5C * 4C2 = 5*6=30
Each group contains 5 letters, which can be arranging in 5! ways.

Therefore required number of words = 30* 5! = 3600

 

 

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Anil Parajuli said: (5:45am on Wednesday 5th August 2015)
5C3*4C2=10*6=6060*5!=7200

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13:  

How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve ?

A.

6

B.

20

C.

60

D.

120

 
 

Option: D

Explanation :

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14:  

In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes ?

A.

1024

B.

625

C.

120

D.

600

 
 

Option: A

Explanation :

Required number of ways are 45=1024.

Since each prize can be distributed in 4 ways

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Jeevan Gyawali said: (12:24pm on Wednesday 16th August 2017)
I don't think the answer is correct in this context. For A to make sense, there needs to be an unlimited supply of the 5 TYPES of prizes. If there are only 5 prizes, the only possible options are :2,1,1,1 -> 4C1 =42,2,1,0 -> 4C2 * 2C1 = 243,1,1,0 -> 4C1 * 3C2 = 123,2,0,0 -> 4C1 * 3C1 = 124,1,0,0 -> 4C1 = 45,0,0,0 -> 4C1 = 4 So, total = 4 24 12 12 12 4 = 68

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15:  

If a five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition, then total number of ways this can be done is

A.

216

B.

240

C.

600

D.

3125

 
 

Option: A

Explanation :

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