Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 !

share|improve this question

1 Answer 1

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 $|X|!$.

2.b) Again I'd suggest that you count the total number (as compute in a)) and then subtract the ones you don't want.

3.Hint: the formula to choose $k$ different elements out of $n$ without order is ${n \choose k}$.

share|improve this answer
    
I assume that this is homework. –  Matt N. May 2 '12 at 11:30

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.