In how many ways can we arrange the number 1,2,3,...,10 so that
1 is not in first place, 2 is not in second place, and so on, and 10 is
not in the 10th place?
a. 1335036. b. 1435036.
c. 1535036. d.1353036.
Answers
Given : arrange the number 1,2,3,...,10 so that 1 is not in first place, 2 is not in second place, and so on, and 10 is not in the 10th place
To Find : Number of Ways
Solution:
The formula for the derangement can be used directly. The number of derangements is
n! (1/2!−1/3!+1/4!+…+(−1)ⁿ/n!)
n = 10
10! ( 1/2! - 1/3! + 1/4! - 1/5! + 1/6! - 1/7! + 1/8! - 1/9! + 1/10!)
= 10!/2! - 10!/3! +10!/4! - 10!/5! + 10!/6! - 10!/7! + 10!/8! - 10!/9! + 10!/10!
= 18,14,400 - 6,04,800 + 1,51,200 - 30240 + 5040 - 720 + 90 - 10 + 1
= 13,34,961
None of the given option is correct
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