# Permutation & Combination wordproblems

I'm studying Permutation & Combination those days and I've got well understanding the whole chapter but those word-problems related to it can't got them well, not even understand any of them. for an example :

1) $X=\{x : x \in Z , -2 \leq x \leq 5 \} , K= \{ (a,b): a,b \in X, a \neq b \}$

Find the number of elements of $K$.

2) If $X=\{3,4,5,6,7\}$, find without repeating any digit, each of the following:

(a) how many $5$-digit numbers can be formed from the elements of $X$?

(b) how many $5$- digit numbers can be formed from the elements of $X$ such that the unit digit is neither $4$ nor $5$?

(c) how many $5$-digit numbers can be formed from the elements of $X$ such that the unit digit is not $4$ and the tens digit is not $5$?

3) In how many ways can each of the following choice be done:

(a) Drawing $2$ playing cards from a pack of $52$ playing cards.

(b) forming football team ($11$ players) from $15$ players.

(c) forming a committee of $3$ Men and $2$ women from among $7$ men and $5$ women.

(d) Distribution of $8$ prizes equally among $4$ persons.

Plus i can't determine which problem to use Permutation & which to use Combination !! any help please !

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In 1) I assume that you mean $X = \{ x \in \mathbb Z \mid -2 \leq x \leq 5 \}$. Then $X = \{-2, -1, 0, 1, 2, 3, 4, 5\}$. The total number of pairs $(a,b)$ then is $|X| \cdot |X| = 64$. Now you need to subtract the number of pairs $(a,a)$. There are $|X|=8$ such pairs, therefore $|K| = 64 - 8 = 56$.
2.a) Asks you in how many ways you can arrange the elements of $X$. The formula to count this is $|X|!$.
3.Hint: the formula to choose $k$ different elements out of $n$ without order is ${n \choose k}$.