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JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

1 of 1

Application +4 | -1

There are

n

points in a plane, no three of which are collinear except '

p

' points all of which are on a line. How many
(a) straight lines can be formed and
(b) triangles can be formed out of these

n

points?

View answer and explanation

Correct option: A

(i)

^n{C_2} - {\,^p}{C_2} + 1

, (ii)

^n{C_3} - {\,^p}{C_3}

Option A ((i)

^n{C_2} - {\,^p}{C_2} + 1

, (ii)

^n{C_3} - {\,^p}{C_3}

) is correct because it accurately calculates the number of straight lines and triangles that can be formed.

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m \times n

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being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is: Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to The number of ways choosing a committee of 4 woman and 5 men from 10 women and 9 men, if Mr.

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{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

n