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4
Q:

In the below word how many words are there in which R and W are at the end positions?

RAINBOW

A) 120 B) 180
C) 210 D) 240

Answer:   D) 240



Explanation:

When R and W are the first and last letters of all the words then we can arrange them in 5!ways. Similarly When W and R are the first and last letters of the words then the remaining letters can be arrange in 5! ways.

Thus the total number of permutations = 2 x 5!  = 2 x 120 = 240

Subject: Permutations and Combinations
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From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?

A) 103336 B) 120000
C) 108336 D) 108333
 
Answer & Explanation Answer: C) 108336

Explanation:

The total possible cases would be a 5 card hand with no restrictions :52C5 5

 

The unwanted cases are:

 

no queens(out of 48 non-queens cards we get 5) 48C5

 

only 1 queen(out of 4 queens we get 1,and out of 48 non-queens we get 4) 4C1*48C4

 

Therefore,52C5-(48C5+4C1*48C4) = 108336

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Q:

From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?

A) 52C5 B) 50C3
C) 52C4 D) 50C4
 
Answer & Explanation Answer: B) 50C3

Explanation:

If the queen of spades and the four of diamonds must be in hand,we have 50 cards remaining out of which we are choosing 3.

 

So, 50C3

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Q:

From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

A) 7250100 B) 7690030
C) 7250000 D) 3454290
 
Answer & Explanation Answer: A) 7250100

Explanation:

There are 13 spades,we must include 2: 13C2

 

There are 13 diamonds,we must include 3: 13C3

 

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts : 26C2

 

Therefore,13C2*13C3*26C2 = 7250100

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Q:

A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?

A) 11P4 B) 11C4
C) 11P5 D) 11C5
 
Answer & Explanation Answer: B) 11C4

Explanation:

If John must be on the committee,we have 11 students remaining,out of which we choose 4. So,11C4

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Q:

How many ways can you select 17 songs for mix CD out of possible 38 songs?

A) 2878 B) 2878 x 10^2
C) 290183753 D) 2878 x 10^10
 
Answer & Explanation Answer: D) 2878 x 10^10

Explanation:

since it is a combination = 38C17 = 2878 x 10^10

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Q:

A pizza can have 3 toppings out of possible 7 toppings.How many different pizza's can be made?

A) 49 B) 35
C) 27 D) 25
 
Answer & Explanation Answer: B) 35

Explanation:

There are 7 toppings in total,and by selecting 3,we will make different types of pizza.

 

This question is a combination since having a different order of toppings will not make a different pizza.

 

So,7C3 =35

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0 5856
Q:

A committee of 4 people is to be formed from a group of 9 people.How many possible committees can be formed?

A) 120 B) 162
C) 126 D) 170
 
Answer & Explanation Answer: C) 126

Explanation:

This question is a combination since order is not important.

 

Answer = 7C3 = 126

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1 4298
Q:

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

A) 53400 B) 17610
C) 11760 D) 45000
 
Answer & Explanation Answer: C) 11760

Explanation:

Required number of ways = 8C5*10C6 =  8C3*10C4 = 11760

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