How many numbers lying between 500 and 600 ca | vedclass

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Question

(A) To form a number between $500$ and $600$,the digit at the hundreds place must be $5$.Since the digits cannot be repeated,we have fixed the hundred

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(A) To form a number between $500$ and $600$,the digit at the hundreds place must be $5$.Since the digits cannot be repeated,we have fixed the hundreds place with the digit $5$.The remaining digits available are ${1, 2, 3, 4, 6}$,which gives us $5$ choices.We need to fill the tens place and the units place using these $5$ remaining digits.The number of ways to arrange $2$ digits out of $5$ is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 5$ and $r = 2$,so $^5P_2 = \frac{5!}{(5-2)!} = \frac{5 	imes 4 	imes 3!}{3!} = 5 	imes 4 = 20$.Therefore,there are $20$ such numbers.

How many numbers lying between $500$ and $600$ can be formed with the help of the digits $1, 2, 3, 4, 5, 6$ when the digits are not to be repeated?

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