Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPermutations3 Marks
Question
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
✓
Answer
Total number of digits = 7 Now, number of 7-digit numbers $=\frac{7!}{3!\ 2!}$ $=\frac{7\times6\times5\times4\times3!}{3!\times2}$ $=7\times6\times5\times2$ $=420$ And, 0 cannot be first digit of the 7-digit numbers $\therefore$ Number of 6-digit numbers $=\frac{6!}{3!\ 2!}$ $=\frac{6\times5\times4\times3!}{3!\times2}$ $=6\times5\times2$ $=60$ Hence, total number of 7-digit number which are greater than 1000000 = 420- 60 = 360.
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