Exchange of coats.

Probability Level 4

6 persons go to a party with their coats. While returning back, only two of them pick up their own coat while rest 4 pick up coats of only other people. So in how many different ways this can happen ?? Extra Credit : 6 people are different and there are only 6 coats

The answer is 135.

1 solution

Pranjal Jain
Nov 29, 2014

Selecting 4 out of 6 person who took wrong coat, $\binom{6}{4}$ . Now number of possible derangements of 4 coats= $D_{4}=4!(\frac{1}{0!}-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!})=9$

So possible ways= $\binom{6}{4}D_{4}=15×9=\boxed{135}$

Is this really a level 5?? @Utsav Singhal

Actually i put level 5 on all . Cuz i have very less followers and i know that it will finally get the lvl down .

Utsav Singhal - 6 years, 6 months ago

You can't increase followers by posting them at level 5. Its better to target the correct 'brilliant' audience. Ones who are at lower levels must get easy ones while ones on higher levels must get better ones! Just an advice! :-P

Pranjal Jain - 6 years, 6 months ago

Thank u !!

Utsav Singhal - 6 years, 6 months ago

Exchange of coats.

The answer is 135.

1 solution

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