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Apititute sum short cut method

If n items are to arranged in a line of which r items must never be together, we can arrange them in (n-r)!r! n−r+1Crn−r+1Cr ways, provided n-r is greater than r. Can someone explain the formulae
here?

RAM took aloan a loan of RS 15000 from laxman it was agree that to pay 8℅simple interest per annum for three years and 10℅compound interest annually on fourth year onwards so how much amount he want to pay at the end if fifth year

statement:- 1) some notebooks are books 2) all books are penciles conclusion:- 1) some notebook are pensciles 2) no pencile is note book . i m confused by the answer that it's either or. how is it possible

whether can i prepare for ibps po/mt within 2 months

how do i solved simplification

https://cracku.in/banking/history/1859921 IN THE GIVEN QUESTION, IA M GETTING THIS TOO AS A POSSIBILITY WHERE AM I WRONG 1-KASHMIR, GUJARAT P,R 2-UP BENGAL,Q,T 3-RAJASTAN, MAHARASHTRA, PUNJAB, W,S,V

https://cracku.in/banking/history/1856884

what type of book I prepare in banking

where r the notes?