Number plates of cars have to made. The first two digits should be alphabets and the next three digits should be numbers. How many number plates can be made such that the number $2$ can only be appeared in the middle of the three digits ( repetition of alphabets and numbers is not allowed)

526500

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482110

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533061

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50000

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Solution

The correct option is A $526500$
The first two places can be filled in $26 \times 25$ ways $= 650$
If $2$ is included then number of ways of filling the three digits $= 9^{2}$ ways
If $2$ is not included then number of ways $= 9^{3}$ ways
Total number of ways $= 650 (81 + 729) = 526500$

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Number plates of cars have to made. The first two digits should be alphabets and the next three digits should be numbers. How many number plates can be made such that the number 2 can only be appeared in the middle of the three digits ( repetition of alphabets and numbers is not allowed)

The correct option is A 526500The first two places can be filled in 26×25 ways =650If 2 is included then number of ways of filling the three digits =92 waysIf 2 is not included then number of ways =93 waysTotal number of ways =650(81+729)=526500

Number plates of cars have to made. The first two digits should be alphabets and the next three digits should be numbers. How many number plates can be made such that the number $2$ can only be appeared in the middle of the three digits ( repetition of alphabets and numbers is not allowed)

The correct option is A $526500$
The first two places can be filled in $26 \times 25$ ways $= 650$
If $2$ is included then number of ways of filling the three digits $= 9^{2}$ ways
If $2$ is not included then number of ways $= 9^{3}$ ways
Total number of ways $= 650 (81 + 729) = 526500$