If S = {1,3,5,7} then which of the following is/are true?

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Sum of all four digit numbers if repetition of digits is not allowed is equal to 3!.16(1111)

Sum of all three digit numbers if repetition of digits is not allowed is equal to 5328

Sum of all four digit numbers if repetition of digits is allowed is equal to 432(1111)

Sum of all the digits in the units place of all four digit numbers if repetition of digits is allowed is equal to 432

answer is A, B, D.

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Detailed Solution

i) $(1111) (1 + 3 + 5 + 7)$ 3!

$ii) (1111) (1 + 3 + 5 + 7) \cdot 3^{3}$

${iii)}^{3} P_{2} (111) (1 + 3 + 5 + 7) \neq 5328$

iv) $3^{3} (1 + 3 + 5 + 7) = 432$

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