A seven-digit number is formed using the digi | vedclass

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(C) The given digits are $3, 3, 4, 4, 4, 5, 5$. Total number of digits is $7$.The total number of $7$-digit numbers that can be formed is given by the

Vedclass · Accepted Answer

$\frac{3}{7}$

Vedclass · Answer

(C) The given digits are $3, 3, 4, 4, 4, 5, 5$. Total number of digits is $7$.The total number of $7$-digit numbers that can be formed is given by the permutation of these digits:$	ext{Total numbers} = \frac{7!}{2! 	imes 3! 	imes 2!} = \frac{5040}{2 	imes 6 	imes 2} = \frac{5040}{24} = 210$.$A$ number is divisible by $2$ if its last digit is even. Here,the only even digit available is $4$.If the last digit is fixed as $4$,we are left with $6$ digits: $3, 3, 4, 4, 5, 5$.The number of such $7$-digit numbers is:$	ext{Favorable numbers} = \frac{6!}{2! 	imes 2! 	imes 2!} = \frac{720}{2 	imes 2 	imes 2} = \frac{720}{8} = 90$.The probability that the number is divisible by $2$ is:$P = \frac{	ext{Favorable numbers}}{	ext{Total numbers}} = \frac{90}{210} = \frac{9}{21} = \frac{3}{7}$.

$A$ seven-digit number is formed using the digits $3, 3, 4, 4, 4, 5, 5$. The probability that the number so formed is divisible by $2$ is ..... .

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