Question

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

Answer 1

Question:

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

Answer:

There are 7 letters in the word CORRECT. There are 2C, 1O, 2R, 1E and 1T.

Answer 2

Answer:

${ \tt{arrangements = {}^{n} p_{r}}}$

• since R is repeated two times:

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

• 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]