NCERT Solutions
Class 11 - Mathematics - Chapter 6: PERMUTATIONS AND COMBINATIONSEXERCISE 6.4
Class 11 - Mathematics - Chapter 6: PERMUTATIONS AND COMBINATIONS
Question. 1
If \( ^nC_8 = ^nC_2 \), find \( ^nC_2 \).
Answer:
\( ^nC_2 = 45 \)
Question. 2
Determine \( n \) if
(i) \( ^{2n}C_3 : ^nC_3 = 12 : 1 \)
(ii) \( ^{2n}C_3 : ^nC_3 = 11 : 1 \)
Answer:
(i) \( n = 5 \)
(ii) \( n = 6 \)
Question. 3
How many chords can be drawn through 21 points on a circle?
Answer:
\( 210 \)
Question. 4
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Answer:
\( 40 \)
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.
Answer:
\( 2000 \)
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.
Answer:
\( 778320 \)
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?
Answer:
\( 3960 \)
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.
Answer:
\( 200 \)
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?
Answer:
\( 35 \)