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Find the value (s) of `r` satisfying the equation `"^69 C_(3r-1)-^(69)C_(r^2)=^(69)C_(r^2-1)-^(69)C_(3r)dot`

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Number of values of r satisfying the equation ,^69C_(3r-1) -^(69)C_(r^2)=^69C_(r^2-1)-^69C_(3r) is

.^(n-1)C_(r)+^(n-1)C_(r-1)=

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

Show that .^(n)C_(r)+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_(r) .

The result of ^(n-1)C_r+^(n-1)C_(r-1)=

Find n and r if .^(n)C_(r):^(n)C_(r+1):^(n)C_(r+2)=1:2:3 .

If (n-r+1)^(n)C_(r-1)=mxx^(n)C_(r) then m=

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=.^(n+2)C_(r)(2lerlen) .

Prove that "^n C_r+^(n-1)C_r+...+^r C_r=^(n+1)C_(r+1) .

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