find the number of permutations in the word barley and football?

Question

first word barley second word football

i have no idea how to do this so please explain EXACTLY how you do it. i have a Ti-84 calculator. please write EVERYTHING that you do.
i sincerly appreciate it. thank you very much!

Answer 1

barley = 6 characters all different. You can choose any of 6 for the first, then any of 5 for the second, and so on. There are 6! = 720 different permutations.

football = 8 characters, but two pairs are the same. There are 8! permutations, but swapping the o's or the l's (or both) yields the same word, so you have to divide by 4 to account for the identical characters. 8!/4 = 10,080

Answer 2

Well, for the word BARLEY, there are 6 letters that you can jumble around.

You can put 6 letters in the first spot, 5 in the next spot, etc.

So, there are 6*5*4*3*2*1 = 6! = 720 different permutations of the word BARLEY.

Now, for the word FOOTBALL, you may think there are 8! permutations, similar to the methodology above for the word BARLEY. But, the letter O and the letter L are repeated twice, so we have to divide out those repeated permutations. Essentially, we have to divide out by 2! twice (once for the O's and once for the L's) since if we switch the L's, for example, we get the same permutation, so we end up over counting.

The number of permutations of the word FOOTBALL is therefore 8!/(2! *2!) = 10,080.