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  4. The number of six digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 so that digits do not repeat and the first and last place are even, is

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Q. The number of six digit numbers that can be formed using the digits $0, 1, 2, 3, 4, 5, 6$ so that digits do not repeat and the first and last place are even, is

Permutations and Combinations

Solution:

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Case-I: When ' 0 ' is not at terminal position
${ }^3 C _2 \cdot 2 ! \cdot{ }^5 C _4 \cdot 4 !=6 \times 120=720 $
Case-II: When 0 is at last place
${ }^3 C _1 \cdot 1 \cdot{ }^5 C _4 \cdot 4 !=3 \times 120=360$
Total number of six digit numbers $=720+360=1080$.