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  • A seven-digit number is in the form of abcdefg (g, f, e,..... etc. are digits at units, tens, hundred place ....etc), where <img alt="a<b<c<d>e>f>g" src="https://entrancecorner.on

A seven-digit number is in the form of abcdefg (g, f, e,..... etc. are digits at units, tens, hundred place ....etc), where a<b<c<d>e>f>g and a, b, c, e, f, g are different digits.The number of such numbers is

 

Option: 1

1980


Option: 2

1116

 


Option: 3

1560


Option: 4

1476


Answers (1)

best_answer

Case (i) : zero not taken 

Now we have to select seven digits from 1,2,3,4,5,6,7,8,9 so ways are { }^9 C_7

From 7 digit select the largest digits as d and from remaining 6 , we can select three digits a, b, c\: \: in { }^6 C_3 ways.

Hence number of such numbers are ={ }^9 \mathrm{C}_7 \cdot{ }^6 \mathrm{C}_3

Case (ii) : zero taken then 

0 must be at last place, then number of such numbers are { }^9 \mathrm{C}_6 .{ }^5 \mathrm{C}_3

So total ways \begin{aligned} { }^9 C_7 \cdot{ }^6 C_3+{ }^9 C_6 \cdot{ }^5 C_3 & ={ }^9 C_2 \cdot{ }^6 C_3+{ }^9 C_3 \cdot C_3 \\ \\& =1560 \end{aligned}

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Nehul

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