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

Find the value of n if ""^54P_(r+3)=6840 xx ""^54P_(r+6)

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

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

Simplify : frac(3^-5 xx 10^-5 xx 125)(5^-7 xx 6^-5)

a^m xx a^n xx a^p = ?

Prove that: ""^(n-1)P_r=(n-r)* ""^(n-1)P_(r-1)

Prove that .^(n-1)P_r+r.^(n-1)P_(r-1)=^nP_r .

Evaluate: (5^-1 xx 2^-1) xx 6^-1

Name the property under multiplication used in each of the following. frac(-4)(5) xx 1 = 1 xx frac(-4)(5) = - frac(4)(5)