# Lecture 4 Permutations and Combinations

“Pain is temporary. Quitting lasts forever.” – Lance Armstrong

# 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?