Zynxu wrote:

Why do we use the combination formula instead of the permutation formula?

Hi

Zynxu,

Question asks:

In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?

Or in other words, we can say in how many ways two parks will be parked in the wrong slot?

For example. car no. 6 and car no. 7 are parked in the wrong slot. This we won't count as 2, rather we will count as 1 way only.

Hence you need to apply combination.

Another way we can think as follows:

Suppose car no. 1 in in the wrong place, so all possible combination for the car no. 1 will be:

(1,2), (1,3), (1,4), (1,5), (1,6), (1,7) --- Total 6 ways.

For car no. 2, the following possibilities are there:

(2,1), (2,3), (2,4), (2,5) (2,6), (2,7) --- Total 6 ways.

Similarly, for all other cars, we'll have 6 such possibilities.

Hence the total number of ways = 7*6 = 42 ways.

But, we are double counting each option. Hence, we need to divide the final answer by 2.

The required number of ways = 42/2 = 21 ways.

Hope this helps.

Thanks.