Questions & Answers

Question

Answers

A. 47

B. \[{\text{48}}\]

C. \[50\]

D. None of these

Answer
Verified

Considering the number which is greater than \[50,000\] contains \[5\] digits.

we also have to take the \[5\] as with digit number because number forms initiating this digits are also greater than \[{\text{50,000}}\]out of which the digit \[6\] is repeated twice in the arrangement of remaining places numbers.

So, the numbers of permutation can be given as \[\dfrac{{{\text{5!}}}}{{{\text{2!}}}} = 60\].

But from these arrangements we also have to reject those numbers which begin with \[3\] as in that such case, the numbers will be less than \[50,000\].

We find all such numbers by fixing \[3\] at extreme left space. So remaining \[4\] digits can be filled in \[\dfrac{{{\text{4!}}}}{{{\text{2!}}}}{\text{ = 12}}\].the division is done because the number six is repeated twice in arrangement.

Hence, required number of ways to obtain the numbers are \[{\text{60 - 12 = 48}}\].

Here we use the concept of permutation. In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

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