Let S be the sample space of all five-digit n | vedclass

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(C) The total number of $5$-digit numbers is $n(S) = 9 	imes 10^4 = 90000$.Let $A$ be the set of numbers that are multiples of $7$ but not divisible

Vedclass · Accepted Answer

$1.0285$

Vedclass · Answer

(C) The total number of $5$-digit numbers is $n(S) = 9 	imes 10^4 = 90000$.Let $A$ be the set of numbers that are multiples of $7$ but not divisible by $5$.Smallest $5$-digit number divisible by $7$ is $10003$.Largest $5$-digit number divisible by $7$ is $99995$.Using the formula $a_n = a + (n-1)d$,we have $99995 = 10003 + (n-1)7$,which gives $n = 12857$.Now,find numbers divisible by both $7$ and $5$,i.e.,divisible by $35$.Smallest $5$-digit number divisible by $35$ is $10010$.Largest $5$-digit number divisible by $35$ is $99995$.$99995 = 10010 + (P-1)35$,which gives $P = 2572$.The number of elements in $A$ is $12857 - 2572 = 10285$.The probability $p = \frac{10285}{90000}$.Therefore,$9p = 9 	imes \frac{10285}{90000} = \frac{10285}{10000} = 1.0285$.

Let $S$ be the sample space of all five-digit numbers. If $p$ is the probability that a randomly selected number from $S$ is a multiple of $7$ but not divisible by $5$,then $9p$ is equal to.

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