| A committee of 5 persons is to be constituted from a group of 6 gents and 8 ladies. If the selection is made randomly, find the probability that there are 3 ladies and 2 gents in the committee |
A) \[\frac{60}{149}\]
B) \[\frac{60}{143}\]
C) \[\frac{47}{140}\]
D) \[\frac{42}{139}\]
Correct Answer: B
Solution :
| 5 person out of 14 can be selected in\[{}^{14}{{C}_{5}}\] ways. |
| 3 ladies out of 8 can be selected in \[{}^{8}{{C}_{3}}\]ways. |
| 2 gents out of 6 can be selected in \[{}^{6}{{C}_{2}}\]ways. |
| \[\therefore \]Required probability\[=\frac{{}^{8}{{C}_{3}}\times {}^{6}{{C}_{2}}}{{}^{14}{{C}_{5}}}\] |
| \[=\frac{8\times 7\times 6}{3\times 2\times 1}\times \frac{6\times 5}{2\times 1}\times \frac{5\times 4\times 3\times 2\times 1}{14\times 13\times 12\times 11\times 10}\] |
| \[=\frac{60}{143}\] |
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