First slide

Combinations

Question

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

Moderate

A

72
B

96
C

90
D

98

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
$\begin{array}{l} =^{3} C_{1} \times^{4} C_{1} \times^{3} C_{1} \times^{2} C_{1} \times^{1} C_{1} \\ = 3 \times 4 \times 3 \times 2 \times 1 = 72 \end{array}$
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
$\begin{array}{l} =^{3} C_{1} \times^{3} C_{1} \times^{2} C_{1} \times^{1} C_{1} \\ = 3 \times 3 \times 2 \times 1 = 18 \end{array}$
Required number of ways = 72 + 18 = 90

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