Math Help!?

Question

There are 22 members on the budget committee that is appinted from the 100 members of the U.S Senate. How many different committees of 22 can be forned from 100 avaliable Senators?

Answer 1

You need to use combinations.

For instance, how many groups of 3 can be made out of a total of 4? And this is the key...without repetition! This is why we are using combinations.

Imagine your numbers were 1,2,3,4

You could have:

1,2,3
1,2,4
2,3,4
3,4,1

This is written as 4 C 3 (Set of 4 and groups of 3)..and the formula uses factorials:

3! means 3 factorial, or 1 x 2 x 3

4! means 4 factorial, or 1 x 2 x 3 x 4

So you would have 4! / 3!(4-3)! = 24 / 6 x 1 = 24 / 6 = 4

In the case of 22 senators out of 100.

This means 100 C 22

And the formula is:

100! / 22! (100-22)! = 7.33 x 10^21

So, there are 7,330,000,000,000,000,000,000 (7.3 quintillion) different ways to arrange 22 people / 100 into groups.

I mean, just imagine!

You could have senators 1-22, 2-23, 3-24,....57-79, and then maybe 1-20,77,86...

You can see how many possibilities there are!

Regards,

Mysstere

Answer 2

C= P (100,22) / 22! = 100 x 99 x 98 x 97 x 96 x 95 x 94 x 93 x 92 x 91 x 90 x 89 x 88 x 87 x 86 x 85 x 84 x 83 x 82 x81 x 80 x 79 / 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =
the answer is over 8 billion ! (don't forget that this problem is a combination, not a permutation)

Answer 3

4

Answer 4

4 be cause it is the highest number of committees that will fit into 100

Answer 5

how many groups of 22 fit in 100
100/22= 4 12/22 or 4 groups of 22 because you can't make another

Answer 6

I think it's 4.5 committees?

100/22=4.545454545454

hope this is right.

Answer 7

4 committees. 5 would be too much(4x22=88, 5x22=110)

Answer 8

hi...i think it should be around 2100 according to the equation.....
[ (total no. of people * total no. of people in the group) - total no. of people]....i might be wrong though!