Find the sum of the all the numbers formed by the digits 2,4,6 and 8 without rep

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Question
Find the sum of the all the numbers formed by the digits 2,4,6 and 8 without repetition. Number may be of any of the form like 2,24,684,4862 ?
Options
A. 133345
B. 147320
C. 13320
D. 145874

Correct Answer

147320

Explanation

Sum of 4 digit numbers = (2+4+6+8) x $P_{3}^{3}$ x (1111) = 20 x 6 x 1111 = 133320

Sum of 3 digit numbers = (2+4+6+8) x $P_{2}^{3}$ x (111) = 20 x 6 x 111 = 13320

Sum of 2 digit numbers = (2+4+6+8) x $P_{1}^{3}$ x (11) = 20 x 3 x 11 = 660

Sum of 1 digit numbers = (2+4+6+8) x $P_{0}^{3}$ x (1) = 20 x 1 x 1 = 20

Adding All , Sum = 147320

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