Question

The chairman of the community bazaar is assigning people to chair committees. How many different
ways can the 6 people be assigned to chair the subcommittees?

Answer 1

Answer:

720.

Step-by-step explanation:

The number of ways in which some particular objects can be arranged and ordered is governed by the concept of Permutation and Combination, which plays a high role in Probability Statistics; however, our concern is simply Permutation, we will soon know how it is.

Now we must know two important terminologies:

Permutation:

The number of arrangements in which the order of the objects matters and cannot be ignored is studied in Permutation. To have a complete knowledge, have a glance over the following example:

If one asks you to rearrange the word 'You' in all possible orders, what will be they? They can be:

Y , O , U

Y, U, O

U, O, Y

U, Y, O

O, Y, U and

O , U, Y

Thus it can be arranged in six possible arrangements. And obviously the particular location of each letter 'Y', 'O', 'U' must be respected, as if not, all arrangements will be treated as one, or in simple words there will be no need to rearrange actually.

Combination:

In this case, we rearrange the elements or objects but the order(particular location) do not need to be respected and can be neglected. Consider the following example:

If one asks you in how many ways can a captain choose his team members, then obviously it does not really matter in which sequence the opted them, i.e. choosing the vice-captain, then wicket keeper etc, it really does not matter.

Thus, in our case, there are six different members, and 6 different chairs of committee. Therefore, which case is this?

The answer is Permutation. As there are six different chairs and six different persons to he placed, thus the order in which the persons are placed can affect their designation or committee.

Now, the actual process comes.

To compute the permutation of some objects i.e. in how many ways they can be assigned their seats, can be calculated by:

Permutation = P = n!

Thus,

P = 6!

And by the knowledge of factorial(!):

P = 6x5x4x3x2x1

P = 720.