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(C) The total number of ways to choose two distinct numbers $a$ and $b$ from the set of integers ${1, 2, \dots, 39}$ is given by the combination formu

Vedclass · Accepted Answer

$\frac{4}{741}$

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(C) The total number of ways to choose two distinct numbers $a$ and $b$ from the set of integers ${1, 2, \dots, 39}$ is given by the combination formula ${}^{39}C_2$. ${}^{39}C_2 = \frac{39 	imes 38}{2} = 39 	imes 19 = 741$. We need to find the pairs $(a, b)$ such that $7a - 9b = 0$,which implies $7a = 9b$. Since $7$ and $9$ are coprime,$a$ must be a multiple of $9$ and $b$ must be a multiple of $7$. Given $1 \le a, b \le 39$,the possible pairs $(a, b)$ are: $(9, 7), (18, 14), (27, 21), (36, 28)$. There are $4$ such favorable pairs. Thus,the probability is $\frac{4}{741}$.

If two numbers $a$ and $b$ are chosen from the set of integers $1$ to $39$,then the probability that those numbers satisfy the equation $7a - 9b = 0$ is

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