a five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. what is the probability that the number is divisible by 4?
Answers
Answered by
5
Total 5 digit numbers that can be formed using 1, 2, 3, 4 and 5 = 5! = 120
a number is divisible by 4 if the number formed by the last two digits is divisible by 4. So the numbers which will be divisible by 4 will have 12, 32, 24 or 52 at its end.
total numbers with 12 at end = 3×2×1 = 6
total numbers with 24 at end = 3×2×1 = 6
total numbers with 32 at end = 3×2×1 = 6
total numbers with 52 at end = 3×2×1 = 6
so total numbers divisible by 4 = 6+6+6+6=24
Probability of the number being divisible by 4 = 24/120 = 1/5
a number is divisible by 4 if the number formed by the last two digits is divisible by 4. So the numbers which will be divisible by 4 will have 12, 32, 24 or 52 at its end.
total numbers with 12 at end = 3×2×1 = 6
total numbers with 24 at end = 3×2×1 = 6
total numbers with 32 at end = 3×2×1 = 6
total numbers with 52 at end = 3×2×1 = 6
so total numbers divisible by 4 = 6+6+6+6=24
Probability of the number being divisible by 4 = 24/120 = 1/5
Similar questions