UPSC NDA 2 2021 Mathematics Solved Paper

(a) Given digits are 3, 5, 7, 9.
Since, the number of ways to find 5-digit numbers =5 !
but using 3,5,7,9 every time one-digit will be repeated.
Hence number of 5-digit numbers with digit 3 repeated =‌

5!

2!

Number of 5-digit numbers with digit 5 repeated =‌

5!

2!

Number of 5-digit numbers with digit 7 repeated =‌

5!

2!

Number of 5-digit numbers with digit 9 repeated =‌

5!

2!

∴ Total 5-digit numbers
=‌

5!

2!

+‌

5!

2!

+‌

5!

2!

+‌

5!

2!

=4×(‌

5×4×3×2!

2!

)
=4×(‌

5×4×3×2!

2!

)
=240