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# Lecture - 4 Chapter 7 Permutations and Combinations

Meaning of Combination, how combination is different from permutations, derivation of rule for combinations through permutations, Shortcuts and special cases of combinations

NCERT Exercise 7.4 |

**Question 1. **If \( ^nC_8 = ^nC_2\), find \( ^nC_2\)

**Question 2. **Determine *n* if**(i). **\( ^{2n}C_3 : ^nC_3 = 12 : 1\)**(ii). **\( ^{2n}C_3 : ^nC_3 = 11 : 1\)

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

Working with AND, OR in Permutations, Combinations and Probability

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

**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.

**Example 19. **What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these **(i)** four cards are of the same suit, **(ii)** four cards belong to four different suits, **(iii)** are face cards, **(iv)** two are red cards and two are black cards, **(v)** cards are of the same colour?

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

**Question 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?

**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.

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