CMAT questions on Modern Math - Permutation & Combination

Asked: how many different tickets are needed so that a passenger can travel from any one of 10 stations to any other.

Key idea: a ticket is defined by an ordered pair (from, to): Station A to Station B is a different ticket from B to A.

Choose the starting station in 10 ways and the destination in 9 ways (any station except the start): \(10 \times 9 = 90\).

Answer: 90

OMEGA has 5 distinct letters: vowels O, E, A (3) and consonants M, G (2).

The odd places are 1, 3 and 5, which is exactly 3 places for the 3 vowels.

• Arrange the vowels in the odd places: 3! = 6 ways.
• Arrange the consonants in places 2 and 4: 2! = 2 ways.

Total = 6 × 2 = 12.

Answer: 12 ways