How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
-
A.
91 -
B.
191 -
C.
291 -
D.
391
Correct Answer: Option C
Explanation
Note that every 4- digit and 5- digit numbers formed is greater than 150. Therefore, (^{5}P_{5} + ^{5}P_{4} = frac{5!}{(5 – 5)!} + frac{5!}{(5 – 4)!} = 120 + 120 = 240) numbers are greater than 150 already.
Among the 3- digit numbers, the numbers 123, 124, 125, 132, 134, 135, 142, 143 and 145 are removed from the ones that meet the criterion so we have:
(^{5}P_{3} – 9 = frac{5!}{(5 – 3)!} = 60 – 9 = 51 implies 240 + 51 = 291) numbers are greater than 150.