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  4. Numbers lying between 999 and 10000 than can be formed from the digits 0, 2, 3, 6, 7, 8 (repetition of digits not allowed) are :

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Q. Numbers lying between 999 and 10000 than can be formed from the digits 0, 2, 3, 6, 7, 8 (repetition of digits not allowed) are :

Permutations and Combinations

Solution:

There are 6 digits (0, 2, 3, 6, 7, 8). Ten thousand place can be filled with 2, 3, 6, 7, 8. Thus 5 digits can be used in constructing the unit place.
Now, from the rest 5 no. we can use only 3 nos. at a time. Then the second digit can be selected in 3! i.e. 6 ways. And the rest no. in $^5C_3$ ways. Thus the total nos. lying between 999 to 10,000 are:
$ 5 \times 3 \times 2 \times \frac{5 \times 4}{2} = 300$.