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Permutations — Maths STD 11 Science — Question

Maharashtra 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?
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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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