Permutation of 15 items taken 7 at a time with replacement

The numerator has four factors beginning with the upper index 5 and going backwards. 5 C 4 =ДЄgain, both the numerator and denominator have the number of factors indicated by the lower index, which in this case is 4. How many combinations are there of 5 distinct things taken 4 at a time? Solution. The lower index k indicates how many of those we are taking.Д®xample 1. The upper index n indicates the number of distinct things. The numerator has 4 factors starting with the upper index and going down, while the denominator is 4. Notice: The numerator and denominator have the same number of factors, 4, which is indicated by the lower index. This is The number of combinations of 10 different things taken 4 at a time. Therefore, the number of combinations is equal to the number of permutations divided by 4!. In other words, there are 4! times as many permutations as combinations. But all of those permutations are one combination. Now, how are the combinations of 10 things taken 4 at a time related to its permutations?ДЄnswer: For any one combination - begh - there are its 4! permutations. That is, we will count all the permuatations of begh. And it does not matter in which order they appear. We care only that 4 particular letters - begh, say - have been selected. Say, however, that the order is not important. If we have 10 letters abcdefgahij, then we have seen that the number of ways to rearrange - permute - any 4 of them is Table of ContentsВ | Home PERMUTATIONS AND COMBINATIONS

Permutation of 15 items taken 7 at a time with replacement