# Thread: help me with new learned topic (permutation & combination)

1. ## help me with new learned topic (permutation & combination)

1. The drama club is staging a play. With 6 men and 8 women auditioning for the leading male and female roles, how many ways can the director cast his leading couple?

2. How many ways are there to pick a King or a Queen from a standard pack of 52 poker cards?
3. A team of 3 students is to be formed from a class of 25 students. How many ways are there to form this team if there is 1 team leader, 1 scribe and 1 timekeeper in the team and each person can only perform one role at a time?
4. How many ways are there to form a three-letter word from “Tuesday”?

P.S. When am I suppose to apply permutation formula? when should I apply combination? i know permutation - order matter combination - order doesn't. but somehow i cant differentiate which to apply when question such as No.3 and 4 come out? can anyone teach me? thanks

2. I kind of have the same problem with these things.

There are more complicated problems that bug me. Those seem quite simple.

For the first one, I think you have 6 * 8. Becase for each one of the 6 men, you have 8 possible women to create a couple, these means 6 * 8.

I don't understand the second problem. You didn't mention any way of picking.

For the third problem, it's probably permutations since order MATTERS here. Why does order matter? Well, if you'd make the team Michael, George and John, you could make George the leader, John the scribe and Michael the timekeeper, or you could make John the leader, Michael the scribe and George the time keeper and so on. Thus, oder matters. The team George/John/Michael is not the same as John/Michael/George.
If you would have to make a team of people where their roles woudn't have mattered, then the team formed by the persons A, B, C would've been the same as the team A, C, B etc. so you would have to use combinations.

For the fourth problem, order matters again as you can form the word "tue" as well as the word "teu" or "etu" etc. using the letters t, u and e. So, again, here is the case of permutations since order matters.

3. 1. The drama club is staging a play. With 6 men and 8 women auditioning for the leading male and female roles, how many ways can the director cast his leading couple?

For every 6 men, you need 8 women, so 6*8 = 48 ways

2. How many ways are there to pick a King or a Queen from a standard pack of 52 poker cards?
There are 4 of Kings and 4 of Queens, so there are only 8 choices, and you can pick one of either King OR Queen, so 8 is the answer.I'm not sure of the explanation.
3. A team of 3 students is to be formed from a class of 25 students. How many ways are there to form this team if there is 1 team leader, 1 scribe and 1 timekeeper in the team and each person can only perform one role at a time?
It's most likely to be permutation as order Matters here.
PERMuTATION = ORDER OF ARRANGEMENT MATTERS
COMBINATION = ORDER OF ARRANGEMENT DOES NOT MATTER
4. How many ways are there to form a three-letter word from “Tuesday”?
This question requires Permutation, you want to form 3-letter word and the order of arrangement is important such as TUE, TEU or DAY, DYA, it's still 3 letters taken from TUESDAY.
I think you can use the Parallel world diagram to help you :

7P3 = 7*6*5 = 210 ways