Q.1)In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Q.2)How many chords can be drawn through 21 points on a circle?
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Answer:
Answer 1 :We have
Number of girls =2
Number of boys =5
∴3 girls out of 4 girls can be selected in
4
C
3
ways and 3 boys out of 5 boys can be selected in
5
C
3
ways.
∴ Required number of ways
5
C
3
×
4
C
3
=
3×2×1
5×4×3
×
3×2×1
4×3×2
=10×4=40
Answer2:
A chord is obtained by joining any two points on a circle. Therefore, total number of chords drawn through 21 points is same as the number of ways of selecting 2 points out of 21 points. This can be done in 21
C
2
ways.
Hence, total number of chords =
21
C
2
=
19!2!
21!
=21×10=210
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