In a circus,there are 10 cages for 10 animals | vedclass

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

Question

(B) Let the $5$ animals that cannot enter the $4$ small cages be called 'large animals' and the other $5$ animals be 'small animals'.There are $6$ lar

Vedclass · Accepted Answer

$86400$

Vedclass · Answer

(B) Let the $5$ animals that cannot enter the $4$ small cages be called 'large animals' and the other $5$ animals be 'small animals'.There are $6$ large cages and $4$ small cages.The $5$ large animals must be placed in the $6$ large cages. This can be done in $_6P_5$ ways.After placing the $5$ large animals,we have $1$ large cage left and $4$ small cages left,totaling $5$ cages for the remaining $5$ small animals.The $5$ small animals can be placed in these $5$ cages in $5!$ ways.Therefore,the total number of ways is $_6P_5 	imes 5!$.$_6P_5 = \frac{6!}{1!} = 6 	imes 5 	imes 4 	imes 3 	imes 2 = 720$.$5! = 120$.Total ways = $720 	imes 120 = 86400$.

In a circus,there are $10$ cages for $10$ animals. $4$ cages are so small that $5$ out of the $10$ animals cannot enter them. In how many ways can the $10$ animals be placed in the $10$ cages?

Similar Questions

All the letters of the word $EAMCET$ are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is

If ${}^n{P_5} = 20 \times {}^n{P_3}$,then $n = $

The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word $INCONSEQUENTIAL$, without repeating any letter, is:

If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

Vedclass Test Series

Exam Paper Generator

Online Exam Module