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Q.9.     In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

9 courses are available and 2 specific courses are compulsory for every student. Therefore, every student has to select 3 courses out of the remaining 7 courses. This can be selected in  ways. Thus, using multiplication priciple, number of ways of selecting courses                                                                                                                                   ...

Q.8.     A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

A bag contains 5 black and 6 red balls. 2 black balls can be selected in   ways and 3 red balls can be selected in  ways. Thus, using multiplication priciple, number of ways of selecting 2 black and 3 red balls                                                                                                                                                                                         ...

Q.7.     In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if  each cricket team of 11 must include exactly 4 bowlers?

Out off, 17 players, 5 are bowlers. A cricket team of 11 is to be selected such that there are exactly 4 bowlers. 4 bowlers can be selected in   ways and 7 players can be selected in  ways. Thus, using multiplication priciple, number of ways of selecting the team                                                                                                                                      ...

Q.6.     Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

In a deck, there is 4 ace out of 52 cards. A combination of 5 cards is to be selected containing exactly one ace. Then, one ace can be selected in  ways and other 4 cards can be selected in  ways. Hence, using the multiplication principle, required the number of 5 card combination                                                                                                                   ...

Q.5.     Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

There are 6 red balls, 5 white balls and 5 blue balls. 9 balls have to be selected in such a way that consists of 3 balls of each colour. 3 balls are selected from 6 red balls in . 3 balls are selected from 5 white balls in  3 balls are selected from 5 blue balls in . Hence, by the multiplication principle, the number of ways of selecting 9 balls                                                 ...

Q.4.     In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

A team of 3 boys and 3 girls be selected from 5 boys and 4 girls. 3 boys can be selected from 5 boys in  ways. 3 girls can be selected from 4 boys in  ways. Therefore, by the multiplication principle, the number of ways in which a team of 3 boys and 3 girls can be selected                                                                                                                            ...

Q.3.     How many chords can be drawn through 21 points on a circle?

To draw chords 2 points are required on the circle. To know the number of chords on the circle , when points on the circle are 21. Combinations =Number of chords

Q.2.     Determine n if

$(ii)\; ^{2n}C_{3}:^{n}C_{3}=11:1$

Given that :                        Thus the value of n=6

Q.2.     Determine n if

$(i)\; ^{2n}C_{3}:^{n}C_{3}=12:1$

Given that :                 The ratio can be written as

Q.1.     If $^{n}C_{8}=^{n}\; \! \! \! \! C_{2},$ find $^{n}C_{2}$

Given :  We know that                                        Thus the answer is 45
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