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6 cartons is an odd number 1 2 3 4 5 6 and feed her to be placed in the envelope so that each envelope contain exactly one card and 2 card is placed in the and the Bear in the same number and moreover the card number one is always placed in the handle of number to then the number of ways it can be done is
6 cartons is an odd number 1 2 3 4 5 6 and feed her to be placed in the envelope so that each envelope contain exactly one card and 2 card is placed in the and the Bear in the same number and moreover the card number one is always placed in the handle of number to then the number of ways it can be done is

```
3 years ago

Arun
25768 Points
```							 Our interest is in finding |T| whereT = {f ∈ S : f(i) is not equal to = i, for i = 2, 3, 4, 5, 6}We classify the functionsin T into types depending upon whether f(2) = 1 or f(2) is not = 1. So, letT1 = {f ∈ T : f(2) = 1}                                (1)and T2 = {f ∈ T : f(2) is not = 1}                 (2)A function in T1 interchanges 1 and 2 and maps the remaining symbols3, 4, 5, 6 to themselves bijectively, without any fixed points. So it islike a derangement of these four symbols. Hence|T1| = D4 = 9                                           (3)as calculated above. Now consider a function f in T2. This correspondsto a bijection from the set {2, 3, 4, 5, 6} to the set {1, 3, 4, 5, 6} in whichf(2) is not = 1 and f(i) is not = i for i = 3, 4, 5, 6. If we relabel the element 1in the codomain as 2 (because we thought that 2 not to go into 1), then f is nothing but a derangement of the fivesymbols 2, 3, 4, 5 and 6. Therefore|T2| = D5 = 60 − 20 + 5 − 1 = 44              (4)Adding (3) and (4) we get|T| = |T1| + |T2| = 9 + 44 = 53
```
3 years ago
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