JEE MATHEMATICS MCQ: COMBINATIONS

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The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is :
]

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Correct option: C

{ }^{21} C_{7}

Option C (

{}^{21}C_7

) is correct because after giving each question a minimum of 2 marks, the remaining marks are distributed among the questions, which can be calculated using combinations.

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A rectangle of dimension

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}}

, then

n

is equal to