1. ## Permutations & Factorials

Hello,

I have a couple of questions I would like help with.

1. In a permutation (nPr), is 'n' always the larger number? For example, there are 5 students and 10 desks, how many permutations are there?

2. 9 people need to be seated. Henry must not sit with Wilson or Nancy. How many permutations will there be?

3. How many different ways can six people be seated at a round table?

4. A committee of three teachers are to select the winner from among ten students nominated for special award. The teachers each make a list of their to three choices in order. The lists have only one name in commo, and that name has a different rnak on each list. In how many ways could th teachers have made their lists?

5. Wayne has a briefcase with a three-digit combination lock. He can set the combintation himself, and his favourite digits are 3, 4, 5, and 7. Each digit can be used at most once.
a) How many permutations of three of these five digits are there?
b) If you think of each permutation as a three digit number, how many of these numbers would be odd numbers?
c) How many of the three-digit numbers are even numbers and begin with a 4?
d) Is there a connection among the four answers above? If so, state what it is and why it occurs.
d) How many of the three-digit

2. I have time for a couple of quick replies:

Originally Posted by NineZeroFive
Hello,

I have a couple of questions I would like help with.

1. In a permutation (nPr), is 'n' always the larger number?

Mr F says: ${\color{red}(nPr) = \frac{n!}{(n-r)!}}$. What happens if n < r ....?

For example, there are 5 students and 10 desks, how many permutations are there?

Mr F says: How many ways can you arrange 10 desks among 5 students ......? (10P5).

2. 9 people need to be seated. Henry must not sit with Wilson or Nancy. How many permutations will there be?

Mr F says: I assume in a row ....? Work out how many arrangements when Henry DOES sit with Wilson or Nancy. Subtact this from the number of arrangements without any restriction.

3. How many different ways can six people be seated at a round table?

Mr F says: You surely have a formula ....... 5!

[snip]
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