Question

Let $x_1,x_2,x_3$ and $x_4$ are the digits chosen from the set $\{0,1,2,3,4,5\}$ and satisfies $x_1<x_2=x_3<x_4$. Number of 4 digit numbers that can be formed is

• A. 10
• B. 8
• C. 7
• D. 4

Answer 1

Answer: (A)

Set 3 digit out of $1,2,3,4,5$ in ${}^5{C}_3$ ways
Say $1,2,4$. Now only one 4 digit number can be formed e.g. 1224
Hence, such numbers are ${}^5{C}_3=10$.