a-man-goes-in-for-an-examination-in-which-there-are-4-papers-which-maxmum-of-10-marks-for-each-paper-the-no-of-ways-of-getting-20-marks-on-the-whole-is-ans-891-

Question Number 50724 by vajpaithegrate@gmail.com last updated on 19/Dec/18

a man goes in for an examination in

which there are 4 papers which maxmum

of 10 marks for each paper the no of ways

of getting 20 marks on the whole is

ans : 891

Answered by ajfour last updated on 19/Dec/18

= c o e f f . o f x^{20} i n {(1 + x + x^{2} + \dots + x^{10})}^{4}

= c o e f f . o f x^{20} i n {(1 - x^{11})}^{4} {(1 - x)}^{- 4}

=^{4 + 20 - 1} C_{3} - 4 (^{4 + 9 - 1} C_{3})

=^{23} C_{3} - 4 (^{12} C_{3})

= \frac{23 \times 22 \times 21}{6} - 4 \times \frac{12 \times 11 \times 10}{6}

= 23 \times 11 \times 7 - 4 \times 2 \times 11 \times 10

= 11 (161 - 80) = 11 \times 81 = 891 .

Commented by vajpaithegrate@gmail.com last updated on 19/Dec/18

thank u sir