Aptitude Day 125

Problems on Permutations and Combinations:

1. A box contains 4 white balls, 2 black balls and 5 red balls. In how many ways can 2 balls be drawn from the box if at least one white ball is to be included in the draw?

Solution:
             = One white ball and one black or red ball + Two white balls
             =  ( ⁴C1 * ⁷C1) + ( ⁴C2)
             = 4*7 + (4*3/1*2)
             =  28 + 6
             = 34.

2. How many 4-digit numbers can be formed from the digits 1, 3, 5, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:
              The unit place must be 5 since the numbers should be divisible by 5.
              Here the possibility is 1.

              The tens place should be any of the remaining 4 numbers.
              Here the possibility is 4.

             The hundreds place should be any of the remaining 3 numbers.
             Here the possibility is 3.

             The thousands place should be any of the remaining 2 numbers.
             Here the possibility is 2.

             The required number of ways = 1*4*3*2 = 24.