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ABCD is a convex quadrilateral and 3, 4,...

ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked on the sides AB, BC, CD, and DA, respectively. The number of triangles with vertices on different sides is a. `270` b. `220` c. `282` d. `342`

A

270

B

220

C

282

D

342

Text Solution

Verified by Experts

The correct Answer is:
D

The no. of triangles with vertices on sides AB, BC, CD is
`.^(3)C_(1)xx^(4)C_(1)xx^(5)C_(1)`
Similarly, for other cases, the total no. of triangle is
`.^(3)C_(1)xx^(4)C_(1)xx^(5)C_(1)+^(3)C_(1)xx^(4)C_(1)xx^(6)C_(1)+^(3)C_(1)xx^(5)C_(1)xx^(6)C_(1)`
`+^(4)C_(1)xx^(5)C_(1)xx^(6)C_(1)=342`
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Knowledge Check

  • PQRS is a quadrilateral having 3 4 5 6 points on PQ , QR, RS and SP respectively. The number of triangles with vertices on different sides is

    A
    220
    B
    270
    C
    282
    D
    none of these

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