7.Find the number of ways of drawing 9 balls from a bag that has 6 red balls 8 green balls and 7 blue was so that three balls of every colour are drawn.
Answer-
Total number ways of balls=8+5+7=18
Number of red balls=6
Number of green balls=5
Number of blue balls=7
9 balls are to be drawn 3 of each colour,
No. of ways of drawing 3 red balls of 6 red balls=$^6C_3$
similarly 3 green balls out of 5 geen balls=$^5C_3$
3 blue ball out of 7 blue balls=$^7C_3$
\therefore $total number ways$=$^6C_3\times^5C_3\times^7C_3$
=$\frac{6!}{3!3!}\times \frac{5!}{3!2!} \times \frac{7!}{3!4!}$
$=20 \times 10 \times 35 $
=7000
8.It. find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.
Answer-
there are 6 boys and 4 girls
we have to select 3 boys out of 6 boys=$^6C_3$
we have to select 2 girls out of 4 girls=$^4C_2$
$\therefore$ total number of ways
=$^6C_3 \times ^4C_2$
$=\frac{6!}{3!3!} \times \frac{4!}{2!2!}$
$=20\times 6$
9. After meeting every participant shake hands with every other participant. If the number of handshakes is 66 find the number of participants in the meeting.
Answer-
Let there be n participants present in the meeting.
A handshake occurs between 2 persons.
∴ Number of handshakes = nC2.
Given 66 handshakes were exchanged.
∴ 66 = nC2
∴ 66 =$\frac{n!}{2!(n-2)!}$
∴ 66 × 2 =$\frac{n(n-1)(n-2)!}{(n-2)!}$
∴ 132 = n(n – 1)
∴ n(n – 1) = 12 × 11
Comparing on both sides, we get
n = 12
∴ 12 participants were present at the meeting.
10. If 20 points are marked on a circle how many chords can be drawn?
Answer-
There are 20 points on a circle.To draw a chord, 2 points are required.
∴ the number of chords that can be drawn through 20 points on the circle.
= 20C2
$=\frac{20!}{{2!18!}$
$=\frac{20×19×18!}{{2×1×18!}$
= 190.
Permutation Combination Exercise 3.1
Permutation Combination Exercise 3.2
Permutation Combination Exercise 3.3
Permutation Combination Exercise 3.4
Permutation Combination Exercise 3.5
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| Permutation and Combination Exercise 3.6 11th Class MH Board |
Permutation and Combination Exercise 3.6 11th Class MH Board
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