# The number of numbers lying betwin 100 and 1000can be formed with the digits 1,2,3,4,5,6,7 is

$\\ \text{Number lying between 100 and 1000 formed by 3 digits.} \\\\ \text{Every digit have 7 option (1,2,3,4,5,6,7) to select a number } \\\\ \text{But repetition is not allowed so number } ={ }^{7} \math{P}_{3}\\$

$\\=\frac{7!}{(7-3)!} \\\\ = \frac{7!}{4!} \\\\=210$

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