There is a group of $5$ children, where two of the children are twins. How many ways can I distribute $6$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

50

Step-by-step explanation:

Suppose that the kids get $x_1,x_2,x_3,x_4,x_4$ pieces of candy, respectively (each twin received $x_4$ pieces). Then we seek all quadruples $(x_1,x_2,x_3,x_4)$ satisfying

\[x_1+x_2+x_3+2x_4 = 6.\]We proceed by casework, based on the number of candies the twins receive.

If $x_4 = 0$, then there are 6 candies to distribute to 3 kids. This is like arranging 6 C's and 2 |'s (dividers), so there are $\binom{8}{2} = 28$ possible distributions.

If $x_4 = 1$, there are 4 candies remaining for the other 3 kids, so there are $\binom{6}{2} = 15$ possible distributions.

If $x_4 = 2$, there are 2 candies remaining, so there are $\binom{4}{2} = 6$ possible distributions.

If $x_4 = 3$, there are 0 candies remaining, for 1 possible distribution.

Adding all of these results from the separate cases, there are a total of

\[28 + 15 + 6 + 1 = \boxed{50}\].

which would be true for stem changing verbs?

they have a consistent spelling change in the stem of the verb.

what is different about the verb “venir” as compared to other stem-changing verbs?

only the third person forms have a stem change.

which of the following could not be considered a “stem-changing” verb?

querer

which of the following would not be condsidered an event?

desfile

what word could be used in response to the following?

¿qué quieres comprar?

quero

what word could be used in response to the following?

¿dónde uds. pueden ir?

vamos  

ellos ir al centro comercial.

yo comprar un vestido.

pedimos

dónde tú?

dormes

step-by-step explanation:

answer:

1.14285714286

step-by-step explanation:

divide 40 into 35 and you will get your answer