Question

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 :

• A. 100
• B. 200
• C. 300
• D. 400

Answer 1

Answer: (C)

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 ${}^5{C}_3$ ways. Thus the total nos. lying between 999 to 10,000 are:
$5\times 3\times 2\times \frac{5\times 4}{2}=300$.