निम्नलिखित का मान ज्ञात कीजिए - `""^(47)C_(4)+sum_(J=1)^(5)""^(52-J)C_(3)`

Explanation

दिया है- `""^(47)C_(4)+underset(J=1)overset(5)sum""^(52-J)C_(3)`
`= ""^(47)C_(4)+""^(51)C_(3)+""^50C_(3)+""^49C_(3)+""^48C_(3)+""^47C_(3)`
`= (""^47C_(3)+""^47C_(4))+""^48C_(3)+""^49C_(3)+""^50C_(3)+""^51C_(3)`
`= (""^48C_(4)+""^48C_(3))+""^49C_(3)+""^50C_(3)+""^51C_(3)" "( :' ^(n)C_(r-1)+""^(n)C_(r)=""^(n+1)C_(r))`
`= (""^(49)C_(4)+""^(49)C_(3))+""^(50)C_(3)+""^(51)C_(3)`
`= (""^(50)C_(4) + ""^(50)C_(3)) + ""^(51)C_(3)`
`= ""^(51)C_(4) + ""^(51)C_(3) = ""^(52)C_(4)`