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

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

Find the values of n and r if ""^nP_r=336,""^nC_r=56 .

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

Find r if 5 xx ^4P_r=6 xx^5P_(r-1) .

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)

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 .

if ^nP_r= ^nP_(r+1) and ^nC_r= ^nC_(r-1) find n and r.

For which values of r, .^nC_r=^nP_r ?