NIMCET 2020 Question Paper with solutions

Question : 1 of 120

Marks: +1, -0

(\table15;8)+ (\table15;7)= (\table n;r)

then the values of n and r are:

Solution:

(\table 15 ; 8 )+(\table 15 ; 7 )=(\table n ; r )

⇒{ }^{15} C _{8}+{ }^{15} C _{7}={ }^{ n } C _{ r }

\;\text " Using "\;{ }^{ n } C _{ r }+{ }^{ n } C _{ r -1}={ }^{ n +1} C _{ r }

⇒{ }^{15} C _{8}+{ }^{15} C _{8-1}={ }^{15+1} C _{8}={ }^{ n } C _{ r }

⇒{ }^{16} C _{8}={ }^{ n } C _{ r }

⇒ n =16 \;\text " and "\; r =8

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