How many numbers are there with 10 as the hamming distance and can be represented using 15 bits.

Question

Hamming distance between two binary numbers is the number of different bits between two numbers. With respect to 0, how many numbers are there with 10 as the hamming distance and can be represented using 15 bits.

Answer 1

For Hamming distance 10 means 10 bit should be different from 15 bit. So there are 15! / 10! * 5! ways to chose 10 bit from 15 bit.

15 X 14 X 13 X 12 X 11
-------------------------------   =  3003
         5 X 4 X 3 X 2 

And 2 value possible for each bit. So total number for Hamming distance 10 = 3003 X 2 = 6006

Comments

Please read some permutation combination basic concept. If things are not clear.
Please let me know If I am wrong .