Four digit numbers are formed using the digits 1,2,3,4, and 6 without repetition. A
number is chosen at random. What is the probability that the number is divisible by 4 ?
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Answer:
Step-by-step explanation:
Total 4 digit numbers formed
4×4×3×2=96
Each of these 96 numbers are equally likely & mutually exclusive of each other.
Now, A number is divisible by 4, if last two digits of the number is divisible by 4
Hence we can have the following numbers in the last two digits
0
4:
first two places can be filled in 3×2=6 ways
1
2:
first two places can be filled in 2×2=4 ways
2
0:
6 ways
2
4:
4 ways
3
2:
4 ways
4
0:
6 ways
Total number of ways=6+4+6+4+4+6=30 ways
probability=
Totaloutcomes
favorableoutcomes
=
96
30
=
16
5
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