Question
The number of four digit numbers that can be formed from the digits 2,3,5,6,7,8 so that the digits do not repeat and the terminal digits are even is ___.
Answer:
:
If the first digit and last digit of the four digit number needs to be even, then we have to choose numbers out of 2, 6 and 8
The first digit can be chosen in 3 ways and the last digit in 2 ways = 3×2=6 ways
The remaining two digits can be chosen and arranged among the remaining 4 digits in 4P2 ways = 12 ways
Total number of ways = 6×12=72 ways
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:
If the first digit and last digit of the four digit number needs to be even, then we have to choose numbers out of 2, 6 and 8
The first digit can be chosen in 3 ways and the last digit in 2 ways = 3×2=6 ways
The remaining two digits can be chosen and arranged among the remaining 4 digits in 4P2 ways = 12 ways
Total number of ways = 6×12=72 ways
Was this answer helpful ?
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