Permutation and Combinations – HSC Math

Posted In: Mathematics
  1. $\n!=\n(\n-1)(\n-2) … … 3.2.1$
  2. i. $^\n\P_\r=\n(\n-1)(\n-2) … … (n-r+1)$
    ii. $^\n\P_\n=\n!$
    iii. $^\n\P_\r={\n!}/{(\n-\r)!}$
  3. $^\n\C_\r=^\n\C_{\n-\r}={\n!}/{{\n!}(\n-\r)!}$
  4. $^\n\C_\r+^\n\C_{\r-1}=^{\n+1}\C_\r$
  5. Number of combination of $\n$ different items taken at least one at a time is $2^n-1$.
  6. i. If $\n$ items are arranges in a cyclic order, number of permutation is $(\n-1)!$
    ii. If teh cycle can be flipped, number of permutation $(\n-1)!/2$
  7. If there are $\n$ items where $\p,\q$ and $\r$ items are alike, then
    $^\n\P_\n={\n!}/{\p!\q!\r!}$

Post Tags: Algebra | HSC


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