Find r if `""^8C_r-""^7C_3=""^7C_2`.

Find r if ""^18C_r=""^18C_(r+2)

Prove that ""^7C_2+""^7C_3=""^8C_3 .

Without expanding show that : |(""^xC_r,""^xC_(r+1),""^xC_(r+2)),(""^yC_r,""^yC_(r+1),""^yC_(r+2)),(""^zC_r,""^zC_(r+1),""^zC_(r+2))|=|(""^xC_r,""^(x+1)C_(r+1),""^(x+2)C_(r+2)),(""^yC_r,""^(y+1)C_(r+1),""^(y+2)C_(r+2)),(""^zC_r,""^(z+1)C_(r+1),""^(z+2)C_(r+2))|

Prove that ""^nC_r+""^nC_(r+1)+""^(n+1)C_(r+2)=""^(n+2)C_(r+2)

Find r in .^15C_r.^15C_(r-1)=11:5 .

Prove that ""^(n-2)C_r+2* ""^(n-2)C_(r-1)+ ""^(n-2)C_(r-2)=""^nC_r

Prove one of the following: ^nC_r+^nC_(r-1)=^(n+1)C_r .

Show that ^nC_r+2. ^nC_(r-1)+ ^nC_(r-2)= ^(n+2)C_r

Prove that .^(n+1)C_(r+1)+^nC_r+^nC_(r-1)=^(n+2)C_(r+1)