Factor Theory Concept ⇒ Consider a composite number n ⇒ n = aᵖbᑫcʳ………..where a, b, c are prime numbers & p, q, r are natural numbers.ThenNumber of factors of n is given...
Selection from identical object/article. The total number of ways of selecting one or more things from ‘p’ identical things of one type, ‘q’ identical things of another type, ‘r’ identical things of another type and ‘n’...
⦿ The total number of combination of n different things taken one or more at a time = 2ⁿ – 1Proof:-Method (1):- Total distinct things = nfor ‘1ˢᵗ’ thing there are 2 ways of selection: included or excludedsimilarly, for ‘2ⁿᵈ’ thing there...
Permutation & Combination PNC Introduction of selection/combination:- Let us assume that Suresh has 5 friends A, B, C, D, E and he want to invite 2 of them for a...
(Q). If k! is not divisible by 1155 then find the maximum value of k (i) 11(ii) 17(iii) 10(iv) 7 Solution:- Since 1155 = 3×5×7×11if we take k as 11 or above then k! will be completely divisible by 1155...
(Q). If p = x¹⁰⁰⁰(1000!) & p is divisible by 10¹⁰⁰⁰. then what would be the minimum number of zeros at the end of p. Solution:- first find number of trailing zeros in...
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