How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?

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Solution: total ways are

.^{6} P_{3} - .^{5} P_{2}

= \frac{6 !}{( 6 - 3 ) !} - \frac{5 !}{( 5 - 2 ) !}

= 6 \cdot 5 \cdot 4 - 5 \cdot 4

= 5 \cdot 5 \cdot 4 = 100

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Question Text	How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?
Answer Type	Text solution:1
Upvotes	150