NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4.
- Permutations and Combinations Class 11 Ex 7.1
- Permutations and Combinations Class 11 Ex 7.2
- Permutations and Combinations Class 11 Ex 7.3
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 11 |
| Subject | Maths |
| Chapter | Chapter 7 |
| Chapter Name | Permutations and Combinations |
| Exercise | Ex 7.4 |
| Number of Questions Solved | 9 |
| Category | NCERT Solutions |
NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4
Ex 7.4 Class 11 Maths Question 1.
lf nC8 = nC2, find nC2.
Solution.
We have, nC8 = nC2
Ex 7.4 Class 11 Maths Question 2.
Determine n if
(i) 2nC3: nC3 =12 : 1
(ii) 2nC3: nC3= 11 : 1
Solution.
Ex 7.4 Class 11 Maths Question 3.
How many chords can be drawn through 21 points on a circle?
Solution.
A chord is formed by joining two points on a circle.
∴ Required number of chords = 2nC2
\(=\frac { 21! }{ 2!19! } =\frac { 21\times 20 }{ 2 } =210\)
Ex 7.4 Class 11 Maths Question 4.
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Solution.
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 = \(\frac { 5! }{ 2!3! } \times \frac { 4! }{ 3!1! } \)
\(=\frac { 5\times 4 }{ 2 } \times 4=40 \)
Ex 7.4 Class 11 Maths 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.
Solution.
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
Ex 7.4 Class 11 Maths 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.
Solution.
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
Ex 7.4 Class 11 Maths 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?
Solution.
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
Ex 7.4 Class 11 Maths 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.
Solution.
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
\(=\frac { 5! }{ 2!3! } \times \frac { 6! }{ 3!3! } =\frac { 5\times 4 }{ 2 } \times \frac { 6\times 5\times 4 }{ 3\times 2 } =200\)
Ex 7.4 Class 11 Maths 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?
Solution.
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 = \(\frac { 7! }{ 3!4! } =\frac { 7\times 6\times 5 }{ 6 } =35\)
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