The figures 4,5, 6, 7,8 are written in every possible order. The number of numbers greater than 56000 is

# The figures 4,5, 6, 7,8 are written in every possible order. The number of numbers greater than 56000 is

1. A

72

2. B

96

3. C

90

4. D

98

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### Solution:

The number forms by the figure 4, 5, 6, 7, 8 which is greater than 56000 is in two cases.
Case I: Let the ten thousand digit place number be greater than 5.
The number of numbers
$\begin{array}{l}{=}^{3}{\mathrm{C}}_{1}{×}^{4}{\mathrm{C}}_{1}{×}^{3}{\mathrm{C}}_{1}{×}^{2}{\mathrm{C}}_{1}{×}^{1}{\mathrm{C}}_{1}\\ =3×4×3×2×1=72\end{array}$
Case ll: Let the ten thousand digit number be 6 and thousand digit number be either 6 or greater than 6.
Then, the number of numbers
$\begin{array}{l}{=}^{3}{\mathrm{C}}_{1}{×}^{3}{\mathrm{C}}_{1}{×}^{2}{\mathrm{C}}_{1}{×}^{1}{\mathrm{C}}_{1}\\ =3×3×2×1=18\end{array}$
Required number of ways = 72 + 18 = 90  Register to Get Free Mock Test and Study Material

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