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There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference.

(i)- How many different ways are there to select a group of four students to attend the conference?

(ii)- If the members of the club decide to send two juniors and two seniors, how many different groupings are possible?


(i): ${^{37}C_4}$ , (ii): ${^{14}C_2}×{^{23}C_2}$


(i): ${^{37}P_4}$ , (ii): ${^{14}P_2}×{^{23}P_2}$


(i): ${^{37}P_4}$ , (ii): ${^{14}C_2}×{^{23}C_2}$


(i): ${^{37}C_4}$ , (ii): ${^{14}P_2}×{^{23}P_2}$

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Option(A) is correct

(i)- Part (i) of the question can be solved by choosing 4 students from the total number of students.

Order is not important.

${^{37}C_4} = \textbf{66, 045}$

(ii)- For part (ii) of the problem choose 2 juniors and 2 seniors.

⇒ ${^{14}C_2} × {^{23}C_2}= 91 × 253$

$= \textbf{23, 023}$

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