Question

Find the value of the combination. 13C5

Answer 1

`_(13)C_5=1287`

Explanation:

`\displaystyle _nC_r=(n!)/(r!(n-r)!)\\\\_(13)C_5=(13!)/(5!(13-5)!)\\\\_(13)C_5=(13!)/(5!\cdot8!)\\\\_(13)C_5=(13*12*11*10*9)/(5*4*3*2*1)\\\\_(13)C_5=(154440)/(120)\\\\_(13)C_5=1287`

Answer 2

GiveN :-

• 
  `\sf \: {}^(13){ C}_(5) \: = 66`

To finD :-

• the value of the Combination = ??

SolutioN :-

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \:`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (13!)/(5!(13 - 5)!) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (13!)/(5!(8)!) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (13!)/(5! * 8!) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (13 * 12 * 11 * 10 * 9 * 8!)/(5! * 8!) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = \frac{13 * 12 * 11 * 10 * 9 * \cancel{8!}}{5! * \cancel{8!}} \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (13 * 12 * 11 * 10 * 9 )/(5 * 4 * 3 * 2 * 1) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (156 * 110 * 9 )/(20 * 6 * 1) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (156 * 990 )/(20 * 6 ) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = (154440 )/(120 ) \\`

`\sf \hookrightarrow \: \: {}^(13){ C}_(5) \: = 1287 \\`