Permutation & Combination · Question 28 · Hard
Permutation & Combination question 28
All arrangements of the letters of the word MOTHER are listed in dictionary (alphabetical) order. What is the position (rank) of the word MOTHER in this list?
- 309
- 287
- 310
- 308
Answer and explanation
Answer: A. 309
Explanation: Letters in order: E, H, M, O, R, T. Words before MOTHER: starting with E or H: 2 × 5! = 240; MO… with E/H third: 2 × 4! = 48; MOT… with E/H/R fourth: 3 × 3! = 18; MOTH with E fifth: 1 × 2! = 2. Rank = 240 + 48 + 18 + 2 + 1 = 309.
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