Menu Close

Category: Permutation and Combination

How-many-possible-solution-sets-that-satisfy-x-1-x-2-x-3-x-4-5-with-0-x-1-3-0-x-2-3-0-x-3-2-0-x-4-2-

Question Number 56913 by Joel578 last updated on 26/Mar/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{possible}\:\mathrm{solution}\:\mathrm{sets}\:\mathrm{that}\:\mathrm{satisfy}\: \\ $$$${x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \:=\:\mathrm{5} \\ $$$$\mathrm{with} \\ $$$$\mathrm{0}\:\leqslant\:{x}_{\mathrm{1}} \:\leqslant\:\mathrm{3}\:\: \\ $$$$\mathrm{0}\:\leqslant\:{x}_{\mathrm{2}} \:\leqslant\:\mathrm{3} \\…

Given-a-set-H-1-2-3-300-We-will-a-create-a-subset-of-H-consisting-of-three-elements-If-the-sum-of-the-three-elements-is-divisible-by-3-then-the-number-of-subsets-that-canbe-made-is-x-Find

Question Number 187948 by horsebrand11 last updated on 24/Feb/23 $$ \\ $$$$\mathrm{Given}\:\mathrm{a}\:\mathrm{set}\:\mathrm{H}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{300}.\:\mathrm{We}\:\mathrm{will}\:\mathrm{a}\right. \\ $$$$\mathrm{cre}{a}\mathrm{te}\:\mathrm{a}\:\mathrm{subset}\:\mathrm{of}\:\mathrm{H}\:\mathrm{consisting}\:\mathrm{of}\: \\ $$$$\mathrm{thre}{e}\:\mathrm{elements}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{thr}{e}\mathrm{e}\:\mathrm{elements}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{subsets}\:\mathrm{that}\: \\ $$$$\mathrm{canbe}\:\mathrm{made}\:\mathrm{is}\:\mathrm{x}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{remaind}{e}\mathrm{r}\:\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{100000} \\…

the-no-of-traingle-formed-by-the-vertices-of-a-decagon-such-that-atleast-one-side-is-in-common-

Question Number 56820 by vajpaithegrate@gmail.com last updated on 24/Mar/19 $$\mathrm{the}\:\mathrm{no}\:\mathrm{of}\:\mathrm{traingle}\:\mathrm{formed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{vertices} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{decagon}\:\mathrm{such}\:\mathrm{that}\:\mathrm{atleast}\:\mathrm{one}\:\mathrm{side} \\ $$$$\mathrm{is}\:\mathrm{in}\:\mathrm{common} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

How-many-odd-numbers-greater-than-60000-can-be-made-from-the-digits-5-6-7-8-9-0-if-no-number-contains-any-digit-more-than-ones-

Question Number 56688 by pieroo last updated on 21/Mar/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{odd}\:\mathrm{numbers},\:\mathrm{greater}\:\mathrm{than} \\ $$$$\mathrm{60000},\:\mathrm{can}\:\mathrm{be}\:\mathrm{made}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digits} \\ $$$$\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{0},\:\mathrm{if}\:\mathrm{no}\:\mathrm{number}\:\mathrm{contains}\:\mathrm{any} \\ $$$$\mathrm{digit}\:\mathrm{more}\:\mathrm{than}\:\mathrm{ones}? \\ $$ Answered by mr W last updated on…

A-box-contains-9-whites-7-red-and-4-blue-balls-Three-balls-are-picked-at-random-one-after-the-other-without-replacement-a-find-the-probability-that-i-they-are-all-of-the-same-color-ii-there-is

Question Number 56678 by pieroo last updated on 21/Mar/19 $$\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{9}\:\mathrm{whites},\:\mathrm{7}\:\mathrm{red}\:\mathrm{and}\:\mathrm{4}\:\mathrm{blue} \\ $$$$\mathrm{balls}.\:\mathrm{Three}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{picked}\:\mathrm{at}\:\mathrm{random}, \\ $$$$\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\:\mathrm{without}\:\mathrm{replacement}. \\ $$$$\left.\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}: \\ $$$$\mathrm{i}.\:\mathrm{they}\:\mathrm{are}\:\mathrm{all}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color} \\ $$$$\mathrm{ii}.\:\mathrm{there}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{each}\:\mathrm{colour} \\ $$$$\mathrm{iii}.\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{red} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{first}\:\mathrm{one}\:\mathrm{picked} \\…

How-many-numbers-greater-than-2000-can-be-formed-using-the-digits-1-3-4-5-6-how-many-of-these-will-be-even-repetition-not-allowed-

Question Number 56624 by pieroo last updated on 19/Mar/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2000} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}? \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{will}\:\mathrm{be}\:\mathrm{even}? \\ $$$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}. \\ $$ Commented by pieroo last updated on 19/Mar/19…

In-how-many-different-ways-can-the-letters-of-the-word-OKINKWO-be-arranged-In-how-many-of-these-arrangements-does-an-O-occupy-both-end-points-of-the-word-

Question Number 56615 by pieroo last updated on 19/Mar/19 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{OKINKWO}\:\mathrm{be}\:\mathrm{arranged}?\: \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{arrangements} \\ $$$$\mathrm{does}\:\mathrm{an}\:\mathrm{O}\:\mathrm{occupy}\:\mathrm{both}\:\mathrm{end}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{word}? \\ $$ Commented by mr W last…