How many different arrangements of the letters in the word BETTER are there?
answers
180
360
720

Question

lgbasallote · Answer

Better has 6 letters

e repeats twice
t repeats twice so..

$$\large \frac{6!}{2!2!} = \frac{6 \times 5 \times 4 \times 3 \times 2}{2\times 2} = \frac{6 \times 5 \times 4 \times 3}{2}$$ can you take it from there?

anonymous · Answer

so you get 720

lgbasallote · Answer

not exactly...you can simplify it further into $$6 \times 5 \times 3 \times 2$$

anonymous · Answer

i mean 360

lgbasallote · Answer

360 is just 6 x 5 x 4 x 3 you have to divide by 2

anonymous · Answer

my bad be cause u divide it by 2

lgbasallote · Answer

so...the final answer is...

anonymous · Answer

no that equal 720

anonymous · Answer

because you have to do 6*5*4*3*2

lgbasallote · Answer

$$\large \frac{6!}{2!2!} = \frac{6 \times 5 \times 4 \times 3 \times 2}{2 \times 2}$$

lgbasallote · Answer

do you get it?

anonymous · Answer

h ok my bad on top you put 6!
                                       -----
                                          2

lgbasallote · Answer

on the bottom it's 4 becaus 2 x 2 is 4

anonymous · Answer

on the bottom not 2*2

lgbasallote · Answer

what do you mean?

anonymous · Answer

u put 2 on the bottom not 2*2

lgbasallote · Answer

oh..that was because i canceled one of the two in the numerator and denominator...so i got $$\large \frac{6 \times 5\times 4 \times 3}{2}$$ see one of the two in the numerator and one of the 2 in the denominator is missing?

anonymous · Answer

ok well thank you