Interview Q&A / Aptitude

1. How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition?

   300. The first digit cannot be 0, so it has 5 choices. The remaining three places use the other 5 digits: 5 x 4 x 3. Total = 5 x 5 x 4 x 3 = 300.

   BeginnerQuick answer1 min read
2. In how many distinct ways can the letters of the word BANANA be arranged?

   60. BANANA has 6 letters with A repeated 3 times and N repeated 2 times, so the count is 6! / (3! x 2!) = 720 / 12 = 60.

   BeginnerQuick answer1 min read
3. In how many ways can 6 people sit around a round table? In how many of these do two particular friends sit together?

   120 ways in total, since circular arrangements of n people number (n - 1)! = 5! = 120. With two friends together, treat them as one unit: (5 - 1)! x 2 = 24 x 2 = 48 ways.

   IntermediateQuick answer1 min read
4. In how many ways can the letters of LEADER be arranged so that the vowels always come together?

   72. Treat the vowels E, A, E as one block. The block plus L, D, R makes 4 units, arranged in 4! = 24 ways. Inside the block, E, A, E arrange in 3!/2! = 3 ways. Total 24 x 3 = 72.

   IntermediateQuick answer1 min read
5. In how many ways can 5 boys and 3 girls stand in a row so that no two girls are next to each other?

   14,400. Arrange the boys first: 5! = 120. They create 6 gaps (including the two ends). Choose and fill 3 of those gaps with the girls in order: 6 x 5 x 4 = 120. Total 120 x 120 = 14,400.

   AdvancedQuick answer1 min read
6. In how many ways can a committee of 5 be formed from 6 men and 4 women so that it has at least 2 women?

   186. Total committees C(10,5) = 252. Subtract those with no woman, C(6,5) = 6, and with exactly one woman, 4 x C(6,4) = 60. 252 - 66 = 186.

   AdvancedQuick answer1 min read