Question

The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1s and exactly three 2s , is equal to

(1) 360

(2) 45

(3) 2520

(4) 1820  

Answer 1

Correct option is: (3) 2520 

Exactly five 1s and exactly three 2s 

\(\Rightarrow\) 2 zeros must be used 

\(\Rightarrow\) 10 places to arrange 5 ones, 3 twos and 2 zeros

\(\Rightarrow \frac{10!}{2!\ 3!\ 5!} = 2520\)