Please look patiently and I don't know if there are any other methods...please feel free to reply if u are unable to understand
720=2×5×3×3×2×2×2=(2^4)×(3^2)×(5^1)
=[(2^0+2^1+2^2+2^3+2^4)]×[(3^0+3^1+3^2)]×[(5^0+5^1)]
No of divisor of 720
=[5terms in 1st bracket ]×[3 terms in 2nd bracket]× [2 terms in last barcket]
=5×3×2=30 i.e there are 30 such no. which divides 720 perfectly
Have a look again,
720=2×5×3×3×2×2×2
Here 5×2 is a divisor of 720 but not multiple of 4.similarly2,3,3×3,5×3,3×2,5,3,2×5×3,2×5×3×3 are also not multiple of 4.So altogether there are 10 divisors of 720 which is not a multiple of 4.
i.e n(E)=10= no of integers which is not the multiple of 4 but divisor if 720
n(S)=30=total 30 divisors of 720
Probability of not getting multiple of 4 when selecting divisors of 720 is,
P'=n(E)/n(S)=10/30=1/3
Then probability of getting multiple of 4 when selecting divisors of 720 is,
P=1-P'=1-1/3=2/3 ANS !!!
