NIMCET 2024 Paper

Section: Mathematics

Question : 6 of 120

Marks: +1, -0

There are 9 bottles labeled

1,2,3, . . ., 9

and 9 boxes labeled

1,2,3, . . ., 9

. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their corresponding numbered boxes is:

$9 ×{ }^9 C _5$
$5 ×{ }^9 C _5$
$25 ×{ }^9 C _5$
$4 ×{ }^9 C _5$

Validate

Solution:

Given that exactly 5 bottles are going to the corresponding numbered boxes, and the remaining 4 are placed in the wrong boxed. This can be done in

{ }^9 C _5 × D_4

, where

D_4

is the derangements of 4 objects. Required answer

={ }^9 C _5 × 9

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