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JEE MATHEMATICS MCQ: COMBINATIONS

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Statement-1 The number of ways distributing 10 identical balls in 4 distinct boxes such that no box is empty, is

{ }^9 C_3

.
Statement-2 The number of ways of choosing any 3 places from 9 different places is

{ }^9 C_3

.

View answer and explanation

Correct option: A

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 because distributing 10 identical balls into 4 distinct boxes with no box empty is equivalent to placing 3 dividers among 9 spaces between the balls, which is

{ }^9 C_3

.

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A rectangle of dimension

m \times n

m

n

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.

A

refuses to serve on the committee when Ms.

B

is a member of the committee, is A man has 7 friends. In how many ways he can invite one or more of them for a tea party? If

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

n