Question

how many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?
A) 128 ways
B) 42 ways
C) 49 ways
D) 14 ways

Answer 1

If all the numbers have to be used each time then there are 7 ways of choosing the first number. After that there are 6 ways of choosing the second number.
Say we choose 4 as the first number, the second could be any of 1,2,3,5,6 or 7
Already we have 42 permutations and we've only got the first two numbers sorted.
We not have 5 numbers left from which to choose the third, and so on. To go all the way down to the last number we end up with
7 x 6 x 5 x 4 x 3 x 2 x 1 permutations. Work it out, it's a big number.

Answer 2

5040?