4 balls are to be selected from a group of 11 bolls. 5 of them are of type A, 2 of them are type B, 2 are of type R, one of type K and one of type D.

Q.In how many ways we can arrange 4 balls out of these 11 balls in a line?

Hello student,
Please find the answer to your question below
TOTAL ARRANGEMENTS OF THESE BALLS 11!/(5!*2!*2!)=83160
4 BALLS CAN BE ALL OF SAME TYPE 1WAY
3sAME 1 DIFFERENT 1*4*4!/3!
2SAME 2DIFFERENT 3*4C2*4!/2!
2 SAME1 TYPE 2SAME ANOTHER TYPE 3C2*4!/2!*2!
all different=5!
1+16+18+216+120
=371