Made Easy Test Series 2019: Combinatory - Permutations And Combinations

Question

in how many ways 6 letters can be placed in 6 envelopes such that at least 4 letters go into their corresponding envelopes ?

Comments

@Shubhanshu

Thanks bro. understood

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@muthu kumar Answer is not 30 bcoz, when you do $^4C_2$ and select say 1,2,3,4, then according to you there are 2 combinations,.. 1,2,3,4,5,6 and 1,2,3,4,6,5 

Now if you select say 3,4,5,6 then also according to you there are 2 combinations..  1,2,3,4,5,6 and 2,1,3,4,5,6

Look here 1,2,3,4,5,6 is repeating..

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Yeah bro. Understood.

Answer 1

Exactly 4 in correct place = 6C4 * D2 = 15

Exactly 5 in correct place = 6C5 * D1 = 6

Exactly 6 in ocrrect place = 1

Total no of ways = 22

Comments

Answer should be 16.

When you consider the case of exactly 5 in correct places, the 6th one is automatically in its correct place.

Therefore, 15+1=16.

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If we have 5 letters in correct places, then 6th one has only 1 place to go, which is its correct place. So answer should be 16