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Words are formed from the letters of EQUATION using 3 vowels and 2 consonants, with no letter used twice. How many such words are possible?

Competition practicePermutations & Combinations

A3600
B7200
C1800
D30

Step-by-Step Solution

EQUATION has vowels E, U, A, I, O and consonants Q, T, N. Choose

^{5} C_{3} \times^{3} C_{2} = 30

, arrange 5 letters in

5! = 120 : 30 \times 120 = 3600

.

Answer: A) 3600

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