Question 49
Permutation and CombinationThe surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begin with O and 9 of the surnames begin with A. 14 of the letters of the alphabet do not appear as the first letter of a surname. If more than one surname begins with a letter besides A and O, how many surnames begin with that letter?
- A.2
- B.3
- C.4
- D.5
- E.6
Show the answer and explanation
Answer: E (6)
Explanation
26 − 14 = 12 letters are used; besides A and O that leaves 10 letters for 40 − 25 = 15 surnames. Each letter has at least one surname, so 9 letters have one each and the remaining letter has 15 − 9 = 6.