Answer:
16C14 = 120
Step-by-step explanation:
we need to find the value of the combination 16C14.
The formula used is [tex]nCr= \frac{n!}{r!(n-r)!}[/tex]
in the given question
n = 16
and r = 14
Putting values and solving:
[tex]16C14= \frac{16!}{14!(16-14)!}\\16C14= \frac{16!}{14!2!}\\16!\,\,can\,\,be\,\,written\,\,as\,\, 16*15*14!\\16C14= \frac{16*15*14!}{14!2!}\\16C14= \frac{16*15}{2*1}\\16C14= \frac{240}{2}\\16C14 = 120[/tex]
So, 16C14 = 120
Answer:
120
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n ! = n(n - 1)(n - 2)...... × 3 × 2 × 1
16[tex]C_{14}[/tex]
= [tex]\frac{16!}{14!2!}[/tex]
= [tex]\frac{16(15)14!}{14!(2)(1)}[/tex] ← cancel 14 !
= [tex]\frac{16(15)}{2}[/tex] = [tex]\frac{240}{2}[/tex] = 120
