Advertisements
Advertisements
Question
How many triangles can be formed by 15 points, in which 7 of them lie on one line and the remaining 8 on another parallel line?
Advertisements
Solution
To form a triangle we need 3 non-collinear points.
Take the 7 points lying on one line be group A and the remaining 8 points lying on another parallel line be group B.
We have the following possibilities
| Group A 7 points |
Group B 8 points |
Combination | |
| (i) | 2 | 1 | 7C2 × 8C1 |
| (ii) | 1 | 2 | 7C1 × 8C2 |
∴ Required number of ways of forming the triangle
= (7C2 × 8C1) + (7C1 × 8C2)
= `(7!)/(2!(7 - 2)!) xx 8 + 7 xx (8!)/(2!(8 - 2)!)`
= `(7!)/(2 xx 5!) xx 8 + 7 xx (8!)/(2! xx 6!)`
= `(7 xx 6 xx 5! xx 8)/(2! xx 5!) + (7 xx 8 xx 7 xx 6!)/(2! xx 6!)`
= `(7 xx 6 xx 8)/(2! xx 5!) + (7 xx 8 xx xx 6!)/(2! xx 6!)`
= `(7 xx 6 xx8)/(2 xx 1) + (7 xx 8 xx 7)/(2 xx 1)`
= 7 × 6 × 4 + 7 × 4 × 7
= 168 + 196
= 364
APPEARS IN
RELATED QUESTIONS
If nPr = 1680 and nCr = 70, find n and r.
Verify that 8C4 + 8C3 = 9C4.
If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.
If a polygon has 44 diagonals, find the number of its sides.
A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when
- atleast two ladies are included.
- atmost two ladies are included.
How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters
- cannot be repeated
- can be repeated
- cannot be repeated but must begin with E
- cannot be repeated but end with CAB.
If nC3 = nC2 then the value of nC4 is:
The number of diagonals in a polygon of n sides is equal to
The value of (5C0 + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5) is:
If nC12 = nC9 find 21Cn
There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?
How many chords can be drawn through 20 points on a circle?
How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
Choose the correct alternative:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines
Choose the correct alternative:
`""^(("n" - 1))"C"_"r" + ""^(("n" - 1))"C"_(("r" - 1))` is
Choose the correct alternative:
The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is
Choose the correct alternative:
The number of rectangles that a chessboard has ______
