In a shooting competition a man can score 5, 4, 3, 2 (or) 0 points for each shot. Then the number of different ways in which he can score 30 in seven shots is ____

Number of ways of making 30 in 7 shots is, Coefficient of $x^{30}in{\left[x^{\theta }+x^2+x^3+x^4+x^5\right]}^7$ Co-efficient of 

$x^{30}in{\left[(1+x^2+x^3)+x^4(1+x)\right]}^7$

$=co.effof{x}^{30}in[7_{C_0}.x^{28}{(1+x)}^7+7_{C_1}$

$x^{24}{(1+x)}^6.(1+x^2+x^3)+7_{C_z}$

$x^{20}{(1+x)}^5.{(1+x^2+x^3)}_1^2\_\_\_\_]$

$=7_{C_0}{.7}_{C_5}+7_{C_1}(6_{C_6}+6_{C_4}+6_{C_3})+7_{C_2}(5_{C_1}+2)$

=21+252+147=420