NDA Math Probability

Total no. of elementary events =63.
Favourable no. of elementary events
= coefficient of x0 in [x+x−1+x0+x−2+x2+x3]3
= coefficient of x0 in[‌‌

1+x+x2+x3+x4+x5

x2

]3
= coefficient of x6 in [1+x+x2+x3+x4+x5]3
= coefficient of x6 in [‌‌

1−x6

1−x

]3
= coefficient of x6 in[1−x6]3[1−x]
= coefficient of x6 in [1−3C1x6+...][1−x]−3
= coefficient of x6 in (1−x)−3⋅3C1 coeff. of x0 in (1−x)−3
=6+3−1C3−1−3C1
=8C2−3C1=‌‌

8!

6!2!

−‌‌

3!

2!

=‌‌

8×7

2

−3=25
Required probability =

25

216