• In how many ways can a chairman, a vice chairman, a secretary, and a treasurer be selected from a committee of ten people?

Is it right that i used the equation 10!/4! ?

I don't know if the answer 151200 is correct. Can someone help me? Thanks!

It would simply be

10 x 9 x 8 x 7 or 5040 ways

This is the same as P(10,4) = 10!/(10-4)!
= 10!/8!
= 5040

Well, it seems you have misunderstood the problem. The equation you mentioned, 10!/4!, would be correct if you were selecting a committee of four from ten people. However, in your case, you are selecting individuals for specific positions: chairman, vice chairman, secretary, and treasurer.

To solve this problem, you need to use the concept of permutations. The number of ways to select individuals for specific positions is found by multiplying the number of choices for each position.

So, let's break it down:

For the chairman position, you have 10 people to choose from.
For the vice chairman position, you have 9 remaining individuals.
For the secretary position, you have 8 remaining individuals.
For the treasurer position, you have 7 remaining individuals.

Multiplying these numbers together, you get:

10 * 9 * 8 * 7 = 5040

So, there are 5040 ways to select a chairman, a vice chairman, a secretary, and a treasurer from a committee of ten people.

I hope that clears things up! Keep up the good work!

To determine how many ways a chairman, a vice chairman, a secretary, and a treasurer can be selected from a committee of ten people, you will need to use the concept of permutations.

The formula to calculate permutations is nPr = n! / (n-r)!, where n is the total number of items to choose from and r is the number of items to be selected.

In this case, you want to select 4 people from a committee of 10. Therefore, the formula becomes 10P4 = 10! / (10-4)!. Simplifying this expression:

10P4 = 10! / 6!
= (10 x 9 x 8 x 7 x 6!) / 6!
= 10 x 9 x 8 x 7
= 5040

So, there are 5040 ways to select a chairman, a vice chairman, a secretary, and a treasurer from a committee of ten people.

Your calculation of 10!/4! is incorrect because it does not account for the arrangement of the selected individuals.

To find the number of ways to select a chairman, a vice chairman, a secretary, and a treasurer from a committee of ten people, you need to use the concept of permutations.

The number of permutations of selecting r objects from a set of n objects is given by the formula nPr = n! / (n-r)!, where "!" denotes factorial.

In this case, you have ten people to choose from and you need to select four positions (chairman, vice chairman, secretary, and treasurer). Therefore, you can use the formula:

10P4 = 10! / (10-4)!

Simplifying:

10P4 = 10! / 6!

Now let's calculate the factorial values:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
6! = 6 × 5 × 4 × 3 × 2 × 1

Plugging in the values:
10P4 = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (6 × 5 × 4 × 3 × 2 × 1)

Canceling out common terms:
10P4 = (10 × 9 × 8 × 7)

Now we can calculate the value:
10P4 = 5,040

So, there are 5,040 ways to select a chairman, a vice chairman, a secretary, and a treasurer from the committee of ten people.

Therefore, the correct answer is not 151,200 but 5,040.

Think of how many ways you can choose a chairman (10), vice-chairman (9 remaining people), secretary(8), treasurer (7).

Multiply them together using the product rule, and the product is
10*9*8*7
=10*9*8*7*6*5*4*3*2*1/(6*5*4*3*2*1)
=10!/(10-4)!