Math Is Fun Forum

Well, this kind of sounds like a new thing to you, but factorial. If you know it, then good, because it involves a lot regarding factorials (yeah, permutations and combinations; my specialty) If you don't, I'm sorry but you'll have to Google it so that you can get used to it

Anyway, let's start the ball rolling, shall we?

(1) Speaking of balls, imagine there are 4 red balls and 6 orange balls. How many ways are there to pick exactly one of each kind?
(2) In an election, there are five presidential candidates, two of which are female. For vice president, there are six candidates, one of which is female. How many ways are there such that females will be president and vice president?
(3) In the game 4 Pics 1 Word, there are twelve letters to choose from. Say we have the letters J, A, S, O, N, A, N, D, I, Y, Y, A and we want to form a five-letter word. How many such ways are possible?
(4) To make a loveteam, there should be names of people, right? Let's say we have the names JULGAT and JASMINE. If we can get two letters from each of the names, how many such ways are there?
(5) In a lottery, there are 6 numbers to be chosen out of 62 numbers. Julgat bet five tickets.
A - 01 07 12 19 24 31
B - 06 21 22 32 41 56
C - 01 08 21 27 36 53
D - 04 08 17 24 37 52
E - 12 17 30 39 49 61

What is the chance of winning the lottery ticket C?