(B) To form a $4-$ digit number using the digits $3, 4, 5,$ and $6$ without repetition,we have $4! = 24$ total numbers.If we fix a digit at the unit's

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(B) To form a $4-$ digit number using the digits $3, 4, 5,$ and $6$ without repetition,we have $4! = 24$ total numbers.If we fix a digit at the unit's place,the remaining $3$ positions can be filled by the remaining $3$ digits in $3! = 6$ ways.Therefore,each of the digits $3, 4, 5,$ and $6$ appears in the unit's place exactly $6$ times.The sum of the digits in the unit's place is:$= (6 \times 3) + (6 \times 4) + (6 \times 5) + (6 \times 6)$$= 6 \times (3 + 4 + 5 + 6)$$= 6 \times 18$$= 108$

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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The sum of the digits in the unit's place of all the $4-$ digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is:

JEE MAIN 2014 All JEE MAIN

A
$432$
B
$108$
C
$36$
D
$18$

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Class 11

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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The sum of the digits in the unit's place of all the $4-$ digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is:

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