In an examination hall,there are mn chairs ar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We have $m$ rows and $n$ columns,making a total of $mn$ chairs.We need to seat $m$ students such that no row is vacant. This means each of the $m$

Vedclass · Accepted Answer

$n^m m!$

Vedclass · Answer

(B) We have $m$ rows and $n$ columns,making a total of $mn$ chairs.We need to seat $m$ students such that no row is vacant. This means each of the $m$ rows must contain exactly one student.First,we choose one chair out of $n$ available chairs in each of the $m$ rows. Since there are $n$ choices for each of the $m$ rows,the number of ways to select the chairs is $n 	imes n 	imes \dots 	imes n$ ($m$ times) $= n^m$.Next,the $m$ students can be arranged in these $m$ selected chairs in $m!$ ways.Therefore,the total number of ways is $n^m 	imes m!$.

In an examination hall,there are $mn$ chairs arranged in $m$ rows and $n$ columns. The number of ways in which $m$ students can be seated such that no row is vacant is:

Similar Questions

Total number of four-digit odd numbers that can be formed using $0, 1, 2, 3, 5, 7$ (repetition is allowed) is:

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

In how many ways can the letters of the word $TRIANGLE$ be arranged such that no two vowels occur together?

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do all the vowels always occur together?

Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module