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In how many ways can 4 people be accommodated in 4 rooms if each room

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Bunuel
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In how many ways can 4 people be accommodated in 4 rooms if each room [#permalink] New post   03 Mar 2021, 06:45
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Question Stats:

56% (01:12) correct 44% (01:57) wrong based on 68 sessions
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In how many ways can 4 people be accommodated in 4 rooms if each room can accommodate from 0 to 4 people inclusive?

A. 24
B. 48
C. 96
D. 192
E. 256
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E
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Mona2019
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Re: In how many ways can 4 people be accommodated in 4 rooms if each room [#permalink] New post   03 Mar 2021, 07:31
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The first person can be accommodated in any of the 4 rooms, so total possible ways for 1st person =4
Similarly , for 2nd,3rd and 4th person - 4 ways each.

So total number of ways = 4*4*4*4=256 ways

IMO E

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Re: In how many ways can 4 people be accommodated in 4 rooms if each room [#permalink] New post   20 Mar 2021, 14:51
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Bunuel wrote:
In how many ways can 4 people be accommodated in 4 rooms if each room can accommodate from 0 to 4 people inclusive?

A. 24
B. 48
C. 96
D. 192
E. 256

Solution:

The first person has 4 choices for a room. The same thing is true for the second, third, and fourth person. Thus, the number of ways to accommodate the 4 people is 4 x 4 x 4 x 4 = 256.

Answer: E
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In how many ways can 4 people be accommodated in 4 rooms if each room [#permalink] New post   17 Apr 2022, 00:25
Mona2019 wrote:
The first person can be accommodated in any of the 4 rooms, so total possible ways for 1st person =4
Similarly , for 2nd,3rd and 4th person - 4 ways each.

So total number of ways = 4*4*4*4=256 ways

IMO E

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Hi thanks for your explanation, I have been following an approach, Can you please point what is wrong with mine?
Approach:
Firstly, I'm writing now all the possibilities of Room accomodation
_n_ represents the room with # of arrangements
_1_ _2_ _3_ _4_
0 0 0 4 - 1
0 0 1 3 - 4
0 0 2 2 - 4C2
0 1 1 2 - 4C2
1 1 1 1 - 4!
Adding up all i got 41 ways..
Can you explain what's wrong with the approach?
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gmatclubot
In how many ways can 4 people be accommodated in 4 rooms if each room [#permalink]
17 Apr 2022, 00:25
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