Five persons entered the lift cabin on the ground floor of an $8$ floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is

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Solution

1st person can leave at any of seven floors in 7 ways

2nd person can leave at any of seven floors in 6 ways

3rd person can leave at any of seven floors in 5 ways

4th person can leave at any of seven floors in 4 ways

5th person can leave at any of seven floors in 3 ways

total ways =7*6*5*4*3 =2520

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Q. Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is
(a)

\frac{{}^{7}P_{5}}{7^{5}}

(b)

\frac{7^{5}}{{}^{7}P_{5}}

(c)

\frac{6}{{}^{6}P_{5}}

(d)

\frac{{}^{5}P_{5}}{5^{5}}

Q. Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them, independently and with equal probability, can leave the cabin at any floor beginning with the first. The probability that all five persons leaving at different floors is

\frac{{^{7} P}_{k}}{7^{5}}

.find the value of

k

Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first. Find out the probability of all five persons leaving at different floors.

Q. Five person entered the left cabin on the ground floor of an eight floor house. Suppose that each of them, independently & with equal probability can leave the cabin at any floor beginning with the first. Find out the probability of all 5 persons leaving at different floors.

Q. 5 persons entered the lift cabin on the ground floor of a

8

floor house (Assume ground floor as also one floor). Assume that each of them independently and with equal probability can leave the cabin at any floor beginning from the first. Find the probability for all the 5 persons to leave the cabin at different floors.

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Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is

1st person can leave at any of seven floors in 7 ways2nd person can leave at any of seven floors in 6 ways3rd person can leave at any of seven floors in 5 ways4th person can leave at any of seven floors in 4 ways5th person can leave at any of seven floors in 3 waystotal ways =7*6*5*4*3 =2520

Five persons entered the lift cabin on the ground floor of an $8$ floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is

1st person can leave at any of seven floors in 7 ways
2nd person can leave at any of seven floors in 6 ways
3rd person can leave at any of seven floors in 5 ways
4th person can leave at any of seven floors in 4 ways
5th person can leave at any of seven floors in 3 ways
total ways =76543 =2520