Ann is grouping 38 rocks. she can put them into group of 10 rocks or as single rocks. what are the different ways ann can group the rocks?

(A) If the rocks are identical, then there are four ways:
38 singles
1 group of 10+28 singles
2 groups of 10+18 singles
3 groups of 10+8 singles

(B) If each rock is different from others then 38 rocks.  In groups of 10 or singles.

Case 0: 0 group+38 singles
1 way

Case 1: 1 group+28 singles:
38C10=38!/(10!(28!))=472733756 ways

case 2:  2 groups of 10+18 singles 38C20*20C10=38!/(20!18!)*20!/(10!10!)/2!=3101868540350580 ways

Case 3: 3 groups of 10+8 singles
38C30*30C20*20C10/3!=45243854529553559880 ways

Total
=1+472733756+3101868540350580+45243854529553559880 
=45246956398566644217 ways
Sorry that it is not possible to enumerate each of the ways, but just the total number of ways.

Hello!

the answer is:

the answer is:

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!