Practice By Tag: Reordering the Letters of a Word

Question: 2014 Fall Final - 7

1 . Consider $m \geq 7$ blue balls $B_1,B_2,\dots,B_m$ and $n \geq 7$ red balls $R_1,R_2,\dots,R_n$. We pick 7 balls of the same color and arrange them on a horizontal line. (The order on the line matters.) How many arrangements are there?

(a)

$m!{m \choose 7} + n!{n \choose 7}$

(b)

$7!{m + n \choose 7}$

(c)

$7!{m \choose 7} + 7!{n \choose 7}$

(d)

None of the above.