Answered

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How many different arrangements are there of the letters in the word CORRECT?

Sagot :

Answer:

[tex]{ \tt{arrangements = {}^{n} p_{r}}}[/tex]

• since R is repeated two times:

[tex]{ \tt{arrangements = \frac{n!}{r _{1}! \: r _{2} } }} \\ \\ { \tt{ = \frac{7!}{2! \: 2! \: 1!} }} \\ \\ = { \tt{ \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(2 \times 1) \times (2 \times 1)\times 1} }} \\ \\ = { \tt{ \frac{5040}{4} }} \\ \\ = { \boxed{ \tt{1260 \: \: arrangements}}}[/tex]

  • n is total number of characters in the word, n = 7
  • r1 is number of characters repeated [ R, T ], r1 = 2
  • r2 is number of characters that appear once [C, O, E, T]
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