Problem
NT-B2-M05-P013 Not Divisible by \(5\)
#13
★★★★☆ Level 4 of 5
Find \(v_5\left(\binom{100}{25}\right)\).
Subtract the exponents in \(100!\), \(25!\), and \(75!\).
\(v_5(100!)=20+4=24\), \(v_5(25!)=5+1=6\), \(v_5(75!)=15+3=18\). The difference is \(24-6-18=0\). Hence \(\binom{100}{25}\) is not divisible by \(5\).
Good counterintuitive example: a large number need not be divisible by \(5\).