A probability problem by Abdullah Ahmed
Probability
Level
pending
Using 1, 2, 3, 4, 5, 6, and 7 once in 7-digit numbers which are not divisible by 5. What is the 2000th number from the lowest to the highest?
The answer is 4315627.
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1 solution
Here for lowest number these 7 digits will be arranged from lower to upper number . If I put 1 in the first position I will get 6! numbers. Among them the number which are divisible by 5 are 5! . So 1 is in 1st place and 5 is not in last place , then total number = 6!-5!=600 Similarly if 2 and 3 takes the first place and 5 is not in the last place then total number = 2 600=1200 So we can take 4 in the first place . Now for rest of the place if 1 is in first position then we get (5!-4!)=96 numbers . So 3 will take the second position cause if 1 and 2 takes then we can find 2 96=192 numbers . If 1 takes the Third position then (4!-3!)=18>8 So 1 takes the 3rd position . If 2 will take 4th position then (3!-2!)=4<8 So 5 will take the 4th palce. If I go through right this I will get 4315672