(Q). In a school 20 students gave gift to each other, then find the total number of gifts.Solution:- 2 student can be selected out of 20 students in ²⁰C₂ ways.& in each pair gifts given are 2.Hence total number of gifts =...
De – arrangement:- Let there are n different colour boxes & correspondingly n different colour balls.Now we are to put these balls into boxes (one in each) such that no two colour matches. = n! – ⁿC₁.(n – 1)! + ⁿC₂.(n – 2)! – ⁿC₃.(n...
Inclusion – Exclusion principle:- Number of ways = (Total number of ways) – (number of ways when restriction fails atleast once) + (Number of ways when restriction fails at least twice) – (Number of ways when restriction fails at least thrice) +...
Application of multinomial in permutation with repetition:- ⦿ Number of selection/combination of r things out of n things of which p are alike of one kind & q are alike of second kind and remaining (n-p-q) things are all different is given by ⟹ coefficient of xʳ...
Special cases of Integral Solution case (1): a + b + c = n condition a>b>c≥0 Number of possible intergral solutions = where [x] → Greatest integer function case (2): a + b + c = n condition a≥b≥c≥0 Number of...
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