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Indian Institute of Technology Patna
Department of Mathematics
Combinatorics (MA522)
Mid-semester Exain (2018-2019)
Pull Marks: 30 Time Limit: 2 Hrs
Let an be the number of subsets of {1,2,...,n} that contain no consecutive integers. Find a
recursive formula for dq. From that formula, find the value for ayo, [442]
Prove by combinatorial arguments that (6)
B) (RE) (+2) 0 (m) _ (net
k k k dT ean
During the month of April, 2017, Indian team played at least one game per day, but not
more than 45 games in that month. Show that there must be a period of some number of
consecutive days during which the team played exactly 14 games. (6)
. How many integers between 0 and 99999 have among their digits each 2,5 and 8? (6)
. Find the number of integral solutions for x1 + #2 +24 + #4 = 18 such that 1 < mz < 5,
“2S 0 $ 4,05 ty <5 and3< 4 <9. (6
