mean? How do you say it?A: You say it like "5 choose 3". If you have 5 things, this is the number of ways you can choose 3 things out of the 5. Mathematically it is:
Q: What does 5! mean? How do you say it?
A: You say it like "5 factorial". It means 5 x 4 x 3 x 2 x 1 = 120.
Q: What does
mean? How do you say it?
A: You say it like "5 choose 3". If you have 5 things, this is
the number of ways you can choose 3 things out of the 5. Mathematically
it is:
You will notice that the numbers in the denominator add up to the number in the numerator. That means the number of ways you can choose 2 things out of 5 is also 10.
Q: How many ways can I arrange the letters in the word
"grape"?
A: Think of each letter as a slot in which you can put a letter.
You have:
5 choices for the 1st slot
4 choices for the 2nd slot
3 choices for the 3rd slot
2 choices for the 4th slot
1 choice for the 5th slot
So, the total number of ways you can arrange the letters in the word
"grape" is 5x4x3x2x1 = 5! = 120. If you're
ever bored some Saturday afternoon with nothing better to do, try
it.
Q: How about the word "potato"?
A: Well, for starters, we have
6! = 720 because there are 6 letters in
"potato". But, the letter 't' appears twice. So, we have to
divide by 2!
because you still have the same arrangement if you switch the two of
them. But, the letter 'o' appears twice as well which means we divide
by 2! again. So the final answer is 720/(2x2) = 180.
Q: So what about "Mississippi" then?
A: Sure, make me think.
There are 11 letters. So 11! = use your calculator
The letter 'i' appears 4 times. So 4!
The letter 's' appears 4 times. So 4!
The letter 'p' appears 2 times. So 2!
So our final answer is:
