so the derivation of NPR R and [Music] NCR NPR we can write as n into n- 1 what is the next value nus 2 and so on to so forth the last value is nus r - 1 now multiply and divide by the term multiply and divide by what is the next value of N - R -1 that is n - R what is the next value N - r + 1 till 1 so multiply this value and divide by this one so n p r which is equal n into n-1 into N - 2 and so on to so forth n- R -1 x value is n - R and then N - r + 1 till 1 the whole divid by n- r into N - r + 1 to 1 you see the numerator n into n -1 N - 2 to 1 and denominator n- R to 1 so the numerator we can write as n factorial and the denominator we can write as nus R factorial so this is called n n p r next the derivation of NCR so actually NP R which is equal to R factorial into NCR what is NPR n factorial divided nus R factorial which is equal R factorial into n c r [Music] so this implies what is NCR NCR which is equal to n factorial / by R factorial into n- R factorial so this is the NPR formula and this one is NCR formula [Music]