A car plate is written by taking 3 alphabets and 3 integers, if after 3 alphabets 3 zeros are not al

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02 Jul 2014 Solve

A car plate is written by taking 3 alphabets and 3 integers, if after 3 alphabets 3 zeros are not allowed, then total possible car plates with no code repeated are ?

OPtion

1) 11232000
2) 17576000
3) 17576
4) 17593576
5) 17558424
6) 14236560
7) 15600000
8) 17568424
9) 12812904
10)None of these

Solution

total alphabets are 26 hence total possibilities for taking 3 alphabets are 26*26*26 = 17576
Total integers are 10 hence total possibilities for taking 3 integers are
10*10*10 = 1000
Total number of avoided cases are 26*26*26*1*1*1 = 17576
Therefore answer is 17576 * 1000 - 17576 = 17558424

Option 5)

Correct Option: 5 Best Solution (8)

Ravi Kumar Kodari   9 years AGO

10^3*26^3-26^3
=17558424

Like? Yes (5) | No (1)  

RAKESH   9 years AGO

26*26*26*10*10*10 - 26*26*26*1
= 26^3 * 999
= 17558424

Like? Yes (5) | No (2)  

Ann Theressa   9 years AGO

out of 26 alphabets 3 are taken (26^3)
out of 10 numbers (0 to 9) 3 are taken (10^3)
after 3 alphabets 3 zeros are not allowed.
===> 26^3 out of total combinations is not allowed.

possible combinations = 26^3 * 10^3 - 26^3
= 17576000-17576
=17558424

option : 5

Like? Yes (4) | No (2)  

Ramesh Sriram   9 years AGO

10^3*26^3-26^3*1
=17558424

Like? Yes (3) | No (1)  

Udhaya kumar   9 years AGO

26^3*10^3 - 26^3 = 17558424

Like? Yes (3) | No (1)  

kapil singh   9 years AGO

3 alphabet = 26*26*26=17576
3 integer no. without(000)=999
so, no. of cars plate =17576*999=17558424

Like? Yes (2) | No (1)  

MRITUNJAY KUMAR   9 years AGO

26^3*10^3-(26^3)=17558424

Like? Yes (2) | No (1)  

kavya   9 years AGO

26 alphabets in 3 aggangements so (26)^3
10 integers in 3 (10)^3-1 since 000 case eliminated so both multiplied together gives 17558424

Like? Yes (1) | No