Question

# The value of $$\displaystyle ^{ 47 }{ { C }_{ 4 } }+\sum _{ r=1 }^{ 5 }{ ^{ 52-r }{ { C }_{ 3 } } }$$ is equal to

A
47C6
B
52C5
C
52C4
D
none of these

Solution

## The correct option is C $$^{ 52 }{ { C }_{ 4 } }$$We need value of $$={ _{ }^{ 47 }{ C } }_{ 4 }^{ }+\sum _{ r=1 }^{ 5 }{ { _{ }^{ 52-r }{ C } }_{ 3 }^{ } }$$$$={ _{ }^{ 47 }{ C } }_{ 4 }^{ }+{ _{ }^{ 51 }{ C } }_{ 3 }^{ }+{ _{ }^{ 50 }{ C } }_{ 3 }^{ }+{ _{ }^{ 49 }{ C } }_{ 3 }^{ }+{ _{ }^{ 48 }{ C } }_{ 3 }^{ }+{ _{ }^{ 47 }{ C } }_{ 3 }^{ }$$$$={ _{ }^{ 51 }{ C } }_{ 3 }^{ }+{ _{ }^{ 50 }{ C } }_{ 3 }^{ }+{ _{ }^{ 49 }{ C } }_{ 3 }^{ }+{ _{ }^{ 48 }{ C } }_{ 3 }^{ }+{ _{ }^{ 47 }{ C } }_{ 3 }^{ }+{ _{ }^{ 47 }{ C } }_{ 4 }={ _{ }^{ 51 }{ C } }_{ 3 }^{ }+{ _{ }^{ 50 }{ C } }_{ 3 }^{ }+{ _{ }^{ 49 }{ C } }_{ 3 }^{ }+{ _{ }^{ 48 }{ C } }_{ 3 }^{ }+{ _{ }^{ 48 }{ C } }_{ 4 }^{ }$$$$={ _{ }^{ 51 }{ C } }_{ 3 }^{ }+{ _{ }^{ 50 }{ C} }_{ 3 }^{ }+{ _{ }^{ 49 }{ C } }_{ 3 }^{ }+{ _{ }^{ 49 }{ C } }_{ 4 }^{ }={ _{ }^{ 51 }{ C } }_{ 3 }^{ }+{ _{ }^{ 50 }{ C } }_{ 3 }^{ }+{ _{ }^{ 50 }{ C } }_{ 4 }^{ }$$$$={ _{ }^{ 51 }{ C } }_{ 3 }^{ }+{ _{ }^{ 51 }{ C } }_{ 4 }^{ }={ _{ }^{ 52 }{ C } }_{ 4 }^{ }$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More