I have this question: An elevator in a building starts with five passengers ands

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I have this question: An elevator in a building starts with five passengers andstops at seven floors. If every passenger is equally likely toget off at each floor and all the passengers leave independently ofeach other, what is the probability that no two passengers will getoff at the same floor?
I know the answer is 7^5 but i don't understand why. Anyinsight would be much appreciated! An elevator in a building starts with five passengers andstops at seven floors. If every passenger is equally likely toget off at each floor and all the passengers leave independently ofeach other, what is the probability that no two passengers will getoff at the same floor?
I know the answer is 7^5 but i don't understand why. Anyinsight would be much appreciated!

Explanation / Answer

the first passenger can get down at any of the seven floors. henceno. of ways first passenger can get down = 7ways the 2nd passenger can get down at any of the seven floors. henceno. of ways 2nd passenger can get down = 7waysthe 3rd passenger can get down at any of the sevenfloors. hence no. of ways 3rd passenger can get down = 7waysthe 4th passenger can get down at any of the sevenfloors. hence no. of ways 4th passenger can get down = 7waysthe 5th passenger can get down at any of the sevenfloors. hence no. of ways 5th passenger can get down = 7ways hence total no. of ways a person can get down = 75 =16807 = total outcome if no two passengers will get off at the same floor, then the first passenger can get down at any of the seven floors. henceno. of ways first passenger can get down = 7ways the 2nd passenger can get down at any of the six floors. hence no.of ways 2nd passenger can get down = 6 waysthe3rd passenger can get down at any of the five floors. hence no. ofways 3rd passenger can get down = 5 waysthe4th passenger can get down at any of the four floors. hence no. ofways 4th passenger can get down = 4 waysthe5th passenger can get down at any of the three floors. hence no. ofways 5th passenger can get down = 3 ways hence no. of ways in which no two passenger get down on same floor= 7x6x5x4x3 = 2520 = favourable outcome hence, probability = favourable outcome / total outcome = 2520 /16807 = 0.1499

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