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Question

In how many ways 6 letters can be placed in 6 envelope such that:
At least 4 letters are placed in correct envelopes

A
16
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B
20
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C
24
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D
25
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Solution

The correct option is A 16
When 4 letters are in correct envelopes, then there is only on possible way in which the remaining two is using envelopes. This is same as selecting four out of side envelopes=6C4=6C64=6C2=15
There are 15 ways in which exactly 4 envelops contain correct letters.
It is not possible to place 5 letters in envelopes correctly because, the 6th letter fits in the correct envelope as well.
Hence there is the only way to place all letters in the correct envelopes.
Total number of ways of placing atleast 4 letters in correct envelopes
=15+1=16 ways.

1214004_1266946_ans_2ed87d6d022442f68c543ecebd1d5cc6.jpg

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