0

Guest

Courses New

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

Grade:11

1 Answers

Arun
25750 Points
6 years ago
 
Our interest is in finding |T| where
T = {f ∈ S : f(i) is not equal to = i, for i = 2, 3, 4, 5, 6}
We classify the functions
in T into types depending upon whether f(2) = 1 or f(2) is not = 1. So, let
T1 = {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 symbols
3, 4, 5, 6 to themselves bijectively, without any fixed points. So it is
like a derangement of these four symbols. Hence
|T1| = D4 = 9                                           (3)
as calculated above. Now consider a function f in T2. This corresponds
to a bijection from the set {2, 3, 4, 5, 6} to the set {1, 3, 4, 5, 6} in which
f(2) is not = 1 and f(i) is not = i for i = 3, 4, 5, 6. If we relabel the element 1
in the codomain as 2 (because we thought that 2 not to go into 1), then f is nothing but a derangement of the five
symbols 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

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More