1.

Compute the""^7C_3+""^6C_4+""6C_3

Answer»

Solution :`""^7C_3+""^6C_4+""^6C_3=""^7C_3+""^6C_4+""^6C_(4-1)`
` =""^7C_3+""^(6+1)C_4 = ""^7C_3+""^7C_4`
`( :'""^nC_r+""^nC_(r-1)=""^(n+1)C_r)`
` = ""^7C_4+""^7C_(4-1)=""^(7+1)C_4`
`= ""^8C_4=(8!)/(4!(8-4)!)=(8*7*6*5)/(4*3*2*1)=70`


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