Q. |
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? |
✔ A. | (i): ${^{37}C_4}$ , (ii): ${^{14}C_2}×{^{23}C_2}$ |
✖ B. | (i): ${^{37}P_4}$ , (ii): ${^{14}P_2}×{^{23}P_2}$ |
✖ C. | (i): ${^{37}P_4}$ , (ii): ${^{14}C_2}×{^{23}C_2}$ |
✖ D. | (i): ${^{37}C_4}$ , (ii): ${^{14}P_2}×{^{23}P_2}$ |
Solution:
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.
⇒ ${^{14}C_2} × {^{23}C_2}= 91 × 253$
$= \textbf{23, 023}$