Question

5. In how many ways can 6 persons occupy 4 vacants
seats?​

Answer 1

Answer:

Step-by-step explanation:

To find: number of arrangements of 5 people in 3 seats.

Consider three seats A B C

Now, place A can be occupied by any 1 person out of 5.

Then place B can be occupied by any 1 person from remaining 4 and for C there are 3 people to occupy the seat.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, permutation of 5 different objects in 3 places is

P(5,3) =  

=  =  = 60.

Therefore, the number of possible solutions is 60.

Answer 2

Answer:

In how many ways can 4 people be seated in a row containing 6 seats? Solution : 1st person can be seated in 6 ways , 2nd person in 5 ways, 3rd person in 4 ways and 4th person in 3 ways. Required number of ways =(6×5×4×3)=360.

Step-by-step explanation:

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