Class 11

Math

Algebra

Permutations and Combinations

There are unlimited number of identical balls of four different colors. How many arrangements of at most $8$ balls in a row can be made by using them?

- $21845$
- $87380$
- $262140$
- none of these

$8$ balls in a row .

$⇒$ Number of ways

$=(4)_{8}+(4)_{7}+(4)_{6}+(4)_{5}+(4)_{4}+(4)_{3}+(4)_{2}+(4)_{1}=4−1(4)_{9}−4 =3262140 =87380$

Therefore number of ways $=87380$