Question

Solve it :-
N=36!×20N=36!×20 in N) is____

Answer 1

Solution -

$N=36!\times 20$

$N=36\times 35\times 34\times ----1\times 20$

Values in multiplication from which

are power of 3 will cone $=\{3,6,12,15,21,24,30,33\}=8$

Two powers 3 will cone $=\{9,18,36\}=3$

There power of 3 will cone $=\left\{27\right\}=1$

Exponent of $3=8\times 1+3\times 2+1\times 3=17$

Values in multiplication from which

one power of 5 will cone $=\{5,10,15,20,20,30,35\}=8$

Two power of 5 will cone $=\left\{25\right\}=1$

Exponent of $5=8\times 1+1\times 2=10$

Exponent 3 in N - Exponent 5 in N $=17-10=17$