How many combinations can be made with a b c d e and f if 5 letters are taken at a time?

Answer 1

The related link explains the difference between a combination (order not important) and a permutation (order is important).

In a combination, the order doesn't matter. This is like drawing 5 cards for a Poker hand. You can arrange them how you want once you have them. Or a lottery ball problem. You can match the balls, regardless of what order they were drawn. Or rolling 5 dice, like in Yatzee.

There's another constraint called repetition. In the dice throwing, you could get all five dice to land on the number 1 (repetition allow). In the card game and lottery ball, once a card or ball is drawn, you cannot draw that one again (no repetition).

In a permutation, order is important. So if you have six Scrabble tiles with your letters A through F, and you want to see how many different five letter words you can make (in this example, for permutations a lot of them would not be real English words, just the certain sequence of letters in a particular order - a permutation).

Then there is permutation with repetition allowed. This is like you draw a tile, record the result, then return that tile into the pile and mix them up and draw again. The order that you recorded is important for permutations.

Depending on which one that you are interested in, there is a formula to calculate. See the related link for explanation of the various formulas.

• So permutation with repetition, the answer is 6^5 = 7776.
• Permutation no repetition: 6! / (6-5)! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
• Combination no repetition: 6! / ((6-5)! * 5!) = 6
• Combination with repetition: (5 + 6 -1)! / (5! * (6-1)!) = 252