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  4. Let x1, x2, x3 and x4 are the digits chosen from the set 0,1,2,3,4,5 and satisfies x1<x2=x3<x4. Number of 4 digit numbers that can be formed is

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Q. 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
Permutations and Combinations

Solution:

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 ${ }^5 C _3=10$.