Question

Find the value of the combination. 16 C 14

Answer 1

Answer:

120

Step-by-step explanation:

Using the definition of n$C_{r}$ = $\frac{n!}{r!(n-r)!}$

where n ! = n(n - 1)(n - 2)...... × 3 × 2 × 1

16$C_{14}$

= $\frac{16!}{14!2!}$

= $\frac{16(15)14!}{14!(2)(1)}$ ← cancel 14 !

= $\frac{16(15)}{2}$ = $\frac{240}{2}$ = 120

Answer 2

Answer:

16C14 = 120

Step-by-step explanation:

we need to find the value of the combination 16C14.

The formula used is $nCr= \frac{n!}{r!(n-r)!}$

in the given question

n = 16

and r = 14

Putting values and solving:

$16C14= \frac{16!}{14!(16-14)!}\\16C14= \frac{16!}{14!2!}\\16!\,\,can\,\,be\,\,written\,\,as\,\, 16*15*14!\\16C14= \frac{16*15*14!}{14!2!}\\16C14= \frac{16*15}{2*1}\\16C14= \frac{240}{2}\\16C14 = 120$

So, 16C14 = 120