Posted by **Gen** on Tuesday, July 25, 2006 at 1:08pm.

Please help with this problem.

In a student writing contest with 25 entries, 3 essays are selected for first, second, and third place awards and 5 are selected for honorable mention. How many ways can this be done? Thanks.

Ok Gen, for the first place there are 25 choices, for second place 24 choices and for third place 23. There are thus 25-times-24-times-23 permutations for the first three places

Would you agree and do you see why?

That leaves 22 remaining from which we can select 5 in any order. That means there are 22 choose 5 combinations for honorable mention.

The total ways this can be done is the product of these two numbers:

(permutations of 25 with 3) times (combinations of 22 choose 5).

Do you see why?

In general, when order matters think permutations. When it doesn't, think combinations.

Thank you Roger. I do understand the order of the first 3, and the non order of the 5. I just did not know that permutations and combinations could be combined. When I do this I get 363,409,200. This is a huge number.Is this correct?

That looks correct by my calculations.

Both permutations and combinations use factorials and these grow very quickly. So numbers this size are common.

Thank you very much Roger.

Find an equation of the line containing the given pair of points (3,5)and (9,8)

assume that there are 4 dimes, 3 nickels, and 2 quarters.

In how many possible ways can the selection be made so that the value of the coins is at least 25 cents?

## Answer this Question

## Related Questions

- math - In a contest the prizes were to be $100 for the first place, $50 for ...
- Geometry - Three different people are to be selected at random, and each will be...
- finite MAth - Assume that the student has a cup with 14 writing implements: 7 ...
- math - Three people are to be selected at random, each will be given one gift ...
- math - Three people are being selected at random, each will be given one gift ...
- English - 1. He won first place in the math contest. 2. He got first place in ...
- college statistics - Three members of a club will be selected to serve as ...
- college mathematics - Three people are to be selected at random, each will be ...
- Finite Math - Assume that the student has a cup with 9 writing implements: 4 ...
- Tree diagrams - Three people are being selected at random, each will be given ...