How many numbers greater than 150 can be formed from the ...
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
91
191
291
391
Correct answer is C
Note that every 4- digit and 5- digit numbers formed is greater than 150. Therefore, 5P5+5P4=5!(5−5)!+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:
5P3−9=5!(5−3)!=60−9=51⟹240+51=291 numbers are greater than 150.
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