Question

Four identical dice are rolled once. Probability that atleast 3 different numbers appear on them is

• A. $\frac{13}{42}$
• B. $\frac{17}{42}$
• C. $\frac{23}{42}$
• D. $\frac{25}{42}$

Answer 1

The correct option is D $\frac{25}{42}$

'aaaa' can appear in ${}^6{C}_1$ ways
'aaab' can appear in $2{(}^6{C}_2)=30$
'aabb' can appear in ${}^6{C}_2=15$
Three numbers appearing :
'aabc' can appear in $3{(}^6{C}_3)=60$
'abcd' can appear in ${}^6{C}_4=15$
Probability =$\frac{60+15}{6+30+15+60+15}=\frac{25}{42}$