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surya_kant_2005

9 persons enter a lift from ground floor of a building which stops in 10 floors (excluding ground floor) . If is known that persons will leave the lift in groups of 2,3 & 4 in different floors. In how many ways this can happen ???

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rashmireddy99

Is the answere 6480? please reply me back.

krishna.gopal

HI SUrya Kant. Sorry for delayed reply. Let us see this problem. As they are 9 persons and they leave in group of 2 , 3 and 4 onle, They will leave lift on three floors only,neither less nor more (here i mean that a group of 2 and another group of 3 will not leave on the same floor as that means 5 persons are leaving on the same floor.)

Number of ways to choose these three floors is ¹⁰C₃ = 120. Once these three floors are chosen number of ways in which they can leave (ie. 234 or 243 or 324 etc) is 3!=6

So total number of ways is 120*6=720

ace

sir but what if they move in 2,2,2,3 thats four floors then wont ur logic be incorrect.

ace

any expert please see this and confirm.

krishna.gopal

Ace see that the question reads "2,3 and 4" people and if we take 2,2,2,3 that and condition is violated as it does not include 4.
If instead another question has "2,3 or 4" then we have to include two more cases to earlier answer (ie 720). They are (2,2,2,3) and (3,3,3). But for this question the answer is 720 only.

Here i would like to tell all of you to please give due emphasis to words in P&C, because a different perception of question will give you a different answer

ace

thank u sir

rashmireddy99

persons in 2,3,4 groups can interchange among themselves why don't u consider those cases?

titun

Hiii,

The solution is easy.

One set of persons ( whether they be 2,3or 4 people) can leave the floor in 10 ways. One of the two remaining sets can leave in 10-1 or 9 ways. The remaining people can leave the lift in 8 ways.

Total no. of ways = 10 x 9 x 8 = 720

einstein

i think nobody counted the no. of ways the groups can be formed and rashmireddy99 is writ to so answer is 907200

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