Six. She has three choices for the first letter, two for the second and one for the third.
3x2x1=6
362,880 ways
15
120 ways
Six.
There are 11!/[2!*2!*2!) = 4,989,600 ways.
6
120 different ways.
If you have three DIFFERENT letters, you can arrange them in 3! = 1 x 2 x 3 = 6 different ways.
Assuming the Ps and Is are indistinguishable: There are 10! / 3! / 3! = 100800 ways If the Ps and Is are distinguishable, then there are 10! = 3628800 ways
You can arrange 4 in 2 ways 1x4 and 2x2.
you can arrange 8 pictures 28 different ways
you can arrange three beads 9 different ways.