Problem Solving

Four persons enter a lift at ground storey of a 7 storey building. In how many ways can they get out of lift on any floor except ground floor.

A 720
B 1296
C 1663
D 360
E 2500


I had come across something similar stating in how many ways 4 letters can be put in 7 different envelopes or 4 rings can be worn in 10 fingers. Please explain in detail the approach and a short way to find the answer. Will post the OA later.

IMO B
each person can get out at any of the 6 floors

so total choices are 6*6*6*6
=1296
I tried it with 2 people and 2 floors it works:)) OA plz

ya OA is B

In the 7 storey building, ground is one, so the remaining floors are (7-1)6 floors. The question is asking us to find out how many ways the 4 persons can get out on any of the 6 floors. There are = 6*6*6*6 = 1296 ways.

Let me take a shot at the other questions you mentioned.

How many ways 4 letters can be put in 7 different envelopes = 7p4 = 840 ways.

How many ways 4 rings can be worn in 10 fingers = 10p4 = 3024 ways.

Vemuri wrote:In the 7 storey building, ground is one, so the remaining floors are (7-1)6 floors. The question is asking us to find out how many ways the 4 persons can get out on any of the 6 floors. There are = 6*6*6*6 = 1296 ways.

Let me take a shot at the other questions you mentioned.

How many ways 4 letters can be put in 7 different envelopes = 7p4 = 840 ways.

How many ways 4 rings can be worn in 10 fingers = 10p4 = 3024 ways.

I think it should be like this:

How many ways 4 letters can be put in 7 different envelopes=7^4

How many ways 4 rings can be worn in 10 fingers=10^4

tohellandback wrote:
I think it should be like this:

How many ways 4 letters can be put in 7 different envelopes=7^4

How many ways 4 rings can be worn in 10 fingers=10^4

Aha...that's right since we are considering all 4 letters to be the same. If the questions were asking:

How many ways 4 different letters can be put in 7 different envelopes, then I guess the answer is 7p4. Is that right?

Vemuri wrote:

tohellandback wrote:
I think it should be like this:

How many ways 4 letters can be put in 7 different envelopes=7^4

How many ways 4 rings can be worn in 10 fingers=10^4

Aha...that's right since we are considering all 4 letters to be the same. If the questions were asking:

How many ways 4 different letters can be put in 7 different envelopes, then I guess the answer is 7p4. Is that right?

Vemuri,
if it is mentioned that "no two letters go in the same envelope", it will be 7p4

tohellandback wrote: Vemuri,
if it is mentioned that "no two letters go in the same envelope", it will be 7p4

That's right. Thank you.

tohellandback wrote:

Vemuri wrote:

tohellandback wrote:
I think it should be like this:

How many ways 4 letters can be put in 7 different envelopes=7^4

How many ways 4 rings can be worn in 10 fingers=10^4

Aha...that's right since we are considering all 4 letters to be the same. If the questions were asking:

How many ways 4 different letters can be put in 7 different envelopes, then I guess the answer is 7p4. Is that right?

Vemuri,
if it is mentioned that "no two letters go in the same envelope", it will be 7p4

hey thanks for clearing this doubt, actually i figured i was calculating my answer to be 7^4 which was not there. but yeah u cleared another thing right here where permutation would have been involved.