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(i) If unit digit is 0 or 5, then the number is division by 5. <br> (ii) If the units digit is 5, then ten thousands digit cannot be zero, now find the number of ways the other four digits can be arranged. <br> (iii) Similarly whe the units digit is 0, the other 4 digits can be arranged in `.^(5)P_(4)` ways. use the fundamental theorem of counting. **What is factorial Zero Factorial examples**

**(a)Compute (i) `(20!)/(18!)` (ii) `(10!)/(6!.4!)` (b)find n if `(n+2)! =2550*n!`**

**fundamental principle of multiplication**

**fundamental principle of addition**

**Difference and application of fundamental principals**

**There are 3 condidates for a Classical; 5 for a Mathematical and 4 for a Natural science scholarship.(i)In how many ways can these scholarship be awarded ? (ii) In how many ways one of these scholarships be awarded?**

**What is permutation ?**

**Notation + theorem :- Let r and n be the positive integers such that `1lerlen`. Then no. of all permutations of n distinct things taken r at a time is given by `(n)(n-1)(n-2).....(n-(r-1))`**

**Prove that `P(n,r)=nP_r=(n!)/((n-r)!`**

**The no. of all permutation of n distinct things taken all at a time is `n!`**