1. ## Combinatorics

1. There are two given sets, the first one with n elements and the second one with m elements. In how many ways can you rearrange all the elements, so that the first p elements are from the first set, and the last q elements are from the second set?

Is my solution correct?

2. How many different n digit numbers can be made with the numbers 3 and 5?

Is the solution solely 2^n, or 2^n - 2 (without counting the n digit 333...3 and 555...5)? The 3 AND 5 confuses me. Do both 3 and 5 have to appear in the number?

2. ## Re: Combinatorics

Originally Posted by MaryLaine
1. There are two given sets, the first one with n elements and the second one with m elements. In how many ways can you rearrange all the elements, so that the first p elements are from the first set, and the last q elements are from the second set?
I would make things clearer: $0<p\le n~,~0<q\le m,~\&~p+q\le n+m$.

Answer: $\left( {{P_p}^n} \right)\left( {{P_q}^m} \right)$ where $\left( {{P_k}^n} \right)$ means a permutation of n items taken k at a time.

Originally Posted by MaryLaine
2. How many different n digit numbers can be made with the numbers 3 and 5?
Is the solution solely 2^n, or 2^n - 2 (without counting the n digit 333...3 and 555...5)? The 3 AND 5 confuses me. Do both 3 and 5 have to appear in the number?
I would answer it as $2^n-2$. But the question needs clarification.

3. ## Re: Combinatorics

Why the permutations but not the variations?