Question 1. lf nC8 = nC2, find nC2.
We have, nC8 = nC2
Question 2. Determine n if
- (i) 2nC3: nC3 =12 : 1
- (ii) 2nC3: nC3= 11 : 1
Question 3. How many chords can be drawn through 21 points on a circle?
A chord is formed by joining two points on a circle.
∴ Required number of chords = 2nC2
Question 4. In how many ways can 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 5C3 ways & 3 girls can be selected from 4 girls in 4C3 ways.
∴ Required number of ways of team selection = 5C3 x 4C3 =
Question 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.
No. of ways of selecting 3 red balls =6C3
No. of ways of selecting 3 white balls = 5C3
No. of ways of selecting 3 blue balls = 5C3
∴ Required no. of ways of selecting 9 balls
Question 6. Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Total no. of cards = 52
No. of ace cards = 4
No. of non-ace cards = 48
∴ One ace card out of 4 can be selected in 4C1 ways.
Remaining 4 cards out of 48 cards can be selected in 48C4ways.
∴ Required no. of ways of selecting 5 cards
Question 7. In Kbw 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?
Total players = 17, No. of bowlers = 5,
No. of non-bowlers = 12
No. of ways of selecting 4 bowlers = 5C4
No. of ways of selecting 7 non-bowlers = 12C7
∴ Required no. of ways of selecting a cricket team
Question 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.
No. of ways of selecting 2 black balls = 5C2
No. of ways of selecting 3 red balls = 6C3
∴ Required no. of ways of selecting 2 black & 3 red balls = 5C2 x 6C3
Question 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?
Total no. of courses = 9
No. of compulsory courses = 2
So, the student will choose 3 courses out of 7 courses [non-compulsory courses].
∴ Required no. of ways a student can choose a programme = 7C3 =