Question

Find the value of the combination. 16 C 14

Answer 1

120

Explanation:

Using the definition of n
`C_(r)` =
`(n!)/(r!(n-r)!)`

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

16
`C_(14)`

=
`(16!)/(14!2!)`

=
`(16(15)14!)/(14!(2)(1))` ← cancel 14 !

=
`(16(15))/(2)` =
`(240)/(2)` = 120

Answer 2

16C14 = 120

Explanation:

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

The formula used is
`nCr= (n!)/(r!(n-r)!)`

in the given question

n = 16

and r = 14

Putting values and solving:

`16C14= (16!)/(14!(16-14)!)\\16C14= (16!)/(14!2!)\\16!\,\,can\,\,be\,\,written\,\,as\,\, 16*15*14!\\16C14= (16*15*14!)/(14!2!)\\16C14= (16*15)/(2*1)\\16C14= (240)/(2)\\16C14 = 120`

So, 16C14 = 120