Find the number of selections that can be made taking 4 letters from the word"ENTRANCE".
(A) 70
(B) 36
(C) 35
(D) 72
(E) 32
(A) 70
(B) 36
(C) 35
(D) 72
(E) 32
(1) All letters are different, means that we have to choose 4 letters form 6 different letters, this can be done in 6C4 = 15GmatKiss wrote:Find the number of selections that can be made taking 4 letters from the word"ENTRANCE".
(A) 70
(B) 36
(C) 35
(D) 72
(E) 32
(2) 2 N's and other letters are different, so 2C2 (2 N's out of 2) * 5C2 (other 2 letters from different 5 letters left) = 10
(3) 2 E's and other letters are different, so 2C2 (2 E's out of 2) * 5C2 (other 2 letters from different 5 letters left) = 10
(4) 2 N's, 2 E's, so 2C2 * 2C2 = 1.
Total number of selections = 15 + 10 + 10 + 1 = 36
The correct answer is B.
