What does the equation 5C3 mean, and its not 5*c*3.?

Question

its like one of those things that are like 6P6 which is 6*5*4*3*2*1 or 6P3 is 6*5*4

Answer 1

It means the number of combinations possible from n = 5 items taken r = 3 items at a time:

Let's find 5C3 taken from abcde.

5C3 from abcde = abc, abd, abe, acd, ace, ade, bcd, bce, bde, cde. That's 10 possible combinations.

nCr = n! / (n - r)! r!

For 5C3, the above evaluates to:

nCr = 5!/ (5 - 3)! 3!
nCr = 5!/ 2! 3!
nCr = (5 * 4 * 3 * 2 *1) / (2 * 1)(3 * 2 * 1)
nCr = 120 / (2 * 6)
nCr = 120 / 12
nCr = 10

Remember that our list of combinations above has 10 elements in it.

Answer 2

5C3 means "5 choose 3". Basically you know that 5P3 could be used when say you have five people and three positions for a job: president, vice president, and manager. In that case, the presidents job is different than the manager's and so on. For this reason, order matters. Being selected as the president is not the same as being selected as the manager.

Now, 5C3 is when order doesnt matter. For example, you want to choose 3 cards from a set of 5 cards. In this case, getting a (lets say) king, queen, and ace is the same as getting a ace, king, queen or king, ace, queen. So in this case order does not matter. This is when you use combination.

The formula for combination is
nCr = n!/((n-r)!r!)
so 5C3 would be 5!/((5-3)!3!) = 10

The formula for permutation is
nPr = n!/r!
so 5P3 = 5!/3! = 20

Also remember that nCr

Answer 3

The answer is 10. If you have a scientific calculator use the nCr button.

The full formula is n! / (n-r)!r!

Answer 4

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