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  4. The number of six digit numbers that can be formed from the digits 1, 2, 3,4, 5, 6,7 so that digits do not repeat and the terminal digits are even, is

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Q. The number of six digit numbers that can be formed from the digits $1, 2, 3,4, 5, 6,7$ so that digits do not repeat and the terminal digits are even, is

Permutations and Combinations

Solution:

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$ 1^{st}$ place can be filled in $3$ ways and 6th place in $2$ ways and rest of the places in $5 \times 4 \times 3 \times 2$ ways.
$\therefore $ Required numbers $= 3 \times 2 \times 5\times 4 \times 3 \times 2 = 720$.