VITEEE 2012 Paper

Required numbers
= 5! [

1

1!

+

1

2!

−

1

3!

+

1

4!

−

1

5!

] = 44
Note that if r (0 ≤ r ≤ n) objects occupy the original places and none of the remaining (n - r) objects occupies its original places then the number of such arrangements =

n

‌

Cr(n−r)! [1−

1

1!

+

1

2!

−

1

3!

+ ... + (−1)n−2

1

(n−r)!

]

or
5 letters 5 directed envelopeAll the of letters Put wrong wrong :
Number of ways =
=[1−‌

1

1!

+‌

1

2!

−‌

1

3!

+‌

1

4!

−‌

1

5!

]5!
=[1−1+‌

1

2

−‌

1

6

+‌

1

24

−‌

1

120

]5!
=[‌

2

6

+‌

4

120

]5!
=[‌

1

3

+‌

1

30

]5!
=[‌

11

30

]120
=44