The number of ways in which we can select thr | vedclass

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(B) The total number of ways to select $3$ numbers from $30$ is given by $^{30}C_3$. Calculating this: $^{30}C_3 = \frac{30 	imes 29 	imes 28}{3 	i

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$3605$

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(B) The total number of ways to select $3$ numbers from $30$ is given by $^{30}C_3$. Calculating this: $^{30}C_3 = \frac{30 	imes 29 	imes 28}{3 	imes 2 	imes 1} = 4060$. There are $15$ even numbers between $1$ and $30$. The number of ways to select $3$ even numbers is $^{15}C_3$. Calculating this: $^{15}C_3 = \frac{15 	imes 14 	imes 13}{3 	imes 2 	imes 1} = 455$. The number of ways to select $3$ numbers such that not all are even is the total ways minus the ways where all are even: $4060 - 455 = 3605$.

The number of ways in which we can select three numbers from $1$ to $30$ such that we exclude every selection consisting of all even numbers is

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