Question

A box contains 5 different red and 3 different
blue balls. Number of ways in which 4 balls be
selected?​

Answer 1

Let us take and as 5 red balls. Let us see if we can split the problem into two steps

Selecting red balls from red balls.

Selecting more balls from the remaining balls.

If the above steps considered are independent of each other, then number of ways of doing them are respectively &

Considering that balls are not identical,

Total ways of selecting 4 balls from 5+4+3 balls is

12C4 = 495

Of those we need to remove the cases where we selected no red ball and only one red ball.

No red ball: 7C4 = 35

Only one red ball: 5C1 x 7C3 = 175

Required answer is 12C4 -( 35 + 175 ) = 285 ways!

Step-by-step explanation: