One mapping (function) is selected at random from all the mappings of the set $A = {1, 2, 3, . . ., n}$ into itself. The probability that the mapping selected is one-one, is

\frac{n!}{n^{n - 1}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{n!}{n^{n}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{n!}{2 n^{n}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

N o n e o f t h e a b o v e

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{n!}{n^{n}}$
Total number of ways mapping is done $= n^{n} (∵ each element in setA can get any value from 1 to n)$

Total Number of ways if mapping is $1 - 1 = n!$

the probability that mapping is $1 - 1 = \frac{n!}{n^{n}}$

Suggest Corrections

Similar questions

One mapping (function) is selected at random from all the mappings of the set A={1,2,3,.....,n} into itself. The probability that the mapping selected is one to one is

Q. One mapping is selected at random from all mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is

(a)

\frac{1}{n^{n}}

(b)

\frac{1}{n!}

(c)

\frac{(n - 1)!}{n^{n - 1}}

(d) None of these

One mapping is selected at random from all the mapping of the set A = {1, 2, 3, ......, n} into itself. The probability that the mapping selected is one to one is

Q. A mapping is selected at random from the set of all the mappings of the set A = {1, 2, …….., n} into itself. The probability that the mapping selected is an injection is:

Join BYJU'S Learning Program

One mapping (function) is selected at random from all the mappings of the set A={1,2,3,...,n} into itself. The probability that the mapping selected is one-one, is

The correct option is B n!nnTotal number of ways mapping is done=nn(∵ each element in setA can get any value from 1 to n)Total Number of ways if mapping is 1−1=n!the probability that mapping is 1−1=n!nn

One mapping (function) is selected at random from all the mappings of the set $A = {1, 2, 3, . . ., n}$ into itself. The probability that the mapping selected is one-one, is

The correct option is B $\frac{n!}{n^{n}}$
Total number of ways mapping is done $= n^{n} (∵ each element in setA can get any value from 1 to n)$

Total Number of ways if mapping is $1 - 1 = n!$

the probability that mapping is $1 - 1 = \frac{n!}{n^{n}}$