Question #19 - How many four-letter arrangements can be made using the letters in the word ALASKA?
I can get the answer in the back (72) by writing out all the ways we can arrange 1 A, 2 As, and 3 As (4, 6, and 4 respectively), and then filling in the blanks using FCP. I'm sure I'm missing a much easier way using nPr and nCr. Can someone show me how to do this in less than 15 steps?
Thanks,
Terry Hogan
case 1: 1A
4! = 24
case 2: 2As
4C2 x 3P2 = 36 (choosing 2 spots to place As) x (picking 2 of the remaining 3 letters)
case 3: 3As
4C3 x 3P1 = 12 (choosing 3 spots to place As) x (picking 1 letter out of 3)
24+36+12=72
I hope this helps
Here is 1 solution
Just considering LSKA 4P4 is 24 ways
considering 3 A's 4 * 3P1 is 12 basically FCP
Considering 2 A's 3C2 any 2 of LSK
4P4 /2 for the 2 A's
4P4 + 4*3P1 + 3C2*4P4/2 = 72 ways
Any other ways???