MathDB
Problems
Contests
National and Regional Contests
India Contests
Mathematics Talent Reward Programme (MTRP)
2013 MTRP Senior
1
MTRP 2013 Senior Paper Question 1
MTRP 2013 Senior Paper Question 1
Source:
January 14, 2024
MTRP
2013
Problem Statement
Find how many committees with a chairman can be chosen from a set of n persons. Hence or otherwise prove that
(
n
1
)
+
2
(
n
2
)
+
3
(
n
3
)
+
.
.
.
.
.
.
+
n
(
n
n
)
=
n
2
n
−
1
{n \choose 1} + 2{n \choose 2} + 3{n \choose 3} + ...... + n{n \choose n} = n2^{n-1}
(
1
n
)
+
2
(
2
n
)
+
3
(
3
n
)
+
......
+
n
(
n
n
)
=
n
2
n
−
1
Back to Problems
View on AoPS