SOLUTION: the digits 4,5,6,7,8,9 are randomly arranged to form a three-digit number. (digits are not repeated) find the probability that the number is even and greater than 900

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Question 385297: the digits 4,5,6,7,8,9 are randomly arranged to form a three-digit number. (digits are not repeated) find the probability that the number is even and greater than 900
Answer by sudhanshu_kmr(1152) (Show Source):
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Total number of 3-digit numbers that can be formed = 6P3 = 120

now we find no. of 3-digit numbers that is even and greater than 900 .......

number should be in this form : 9XE
where E is an even number and X is any digit except 9 and digit on E.

no. of ways to put an even digit at E i.e third place = 3 (4,6 or 8)
no. of ways to put any digit at X i.e second place= 4
(except 9 and which at E )
no. of ways to put 9 at first place = 1

total no. = 1* 3 * 4 = 12

thus, required probability = 12/120 = 1/10
= 0.1