Problem
NT-B2-M05-P008 A Binomial Coefficient
#8
★★★☆☆ Level 3 of 5
Find \(v_3\left(\binom{30}{10}\right)\).
Use \(\binom{30}{10}=30!/(10!20!)\).
\(v_3(30!)=10+3+1=14\), \(v_3(10!)=3+1=4\), \(v_3(20!)=6+2=8\). Therefore \(v_3\left(\binom{30}{10}\right)=14-4-8=2\).
Exponents in a quotient are subtracted.