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In how many ways can 6 boys be allotted into 5 rooms such that no room 12 May 2020, 07:13
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E
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85% (hard)

Question Stats:

53% (02:30) correct 47% (02:04) wrong based on 155 sessions

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In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

A. 27
B. 720
C. 840
D. 900
E. 1800


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E
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In how many ways can 6 boys be allotted into 5 rooms such that no room 12 May 2020, 07:23
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Bunuel
In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

A. 27
B. 720
C. 840
D. 900
E. 1800


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So, first we choose two boys who would stay together =>6C2
Now we have rooms and 5 different groups, 2, 1, 1, 1, 1....These 5 can be accommodated in 5! ways.

Total ways = \(6C2*5!=\frac{6*5}{2}*120=15*120=1800\)

E
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In how many ways can 6 boys be allotted into 5 rooms such that no room 12 May 2020, 07:27
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Bunuel
In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

A. 27
B. 720
C. 840
D. 900
E. 1800


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For 6 boys to be placed in 5 rooms, 1 room will have 2 boys.

choose 2 out of 6 boys: 6C2 = 15

5 rooms can be permuted in 5! ways

Therefore, 5*4*3*2*1*15 = 1800

Correct answer = E
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In how many ways can 6 boys be allotted into 5 rooms such that no room 16 Apr 2022, 10:34
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Bunuel
In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

A. 27
B. 720
C. 840
D. 900
E. 1800


Are You Up For the Challenge: 700 Level Questions
Show more

For no room to be empty, 2 boys will be allotted to 1 room and the remaining 4 rooms will have 1 boys each.
Ways to allocate 2 boys to 1st room = 6C2 = 15
Ways to allocate 1 boy to 2nd room = 4C1
Ways to allocate 1 boy to 3rd room = 3C1
Ways to allocate 1 boy to 4th room = 2C1
Ways to allocate 1 boy to 5th room = 1C1

Total ways = 15*4*3*2 = 360
Since any one of the 5 rooms can hold 2 boys,multiply result by 5 = 360*5 = 1800
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In how many ways can 6 boys be allotted into 5 rooms such that no room 16 Feb 2025, 10:02
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