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Category: Permutation and Combination

How-many-words-with-at-least-2-letters-can-be-formed-from-UNUSUALNESS-

Question Number 130193 by mr W last updated on 23/Jan/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{words}\:\mathrm{with}\:\mathrm{at}\:\mathrm{least}\:\mathrm{2}\:\mathrm{letters} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\boldsymbol{\mathrm{UNUSUALNESS}}? \\ $$ Answered by benjo_mathlover last updated on 23/Jan/21 $$\:\mathrm{U}=\mathrm{3},\:\mathrm{N}=\mathrm{2},\:\mathrm{S}=\mathrm{3},\left(\mathrm{A}=\mathrm{L}=\mathrm{E}=\mathrm{1}\right) \\ $$$$\:\mathrm{words}\::\:\mathrm{XX}\:=\:\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\end{pmatrix}\:=\:\mathrm{3}…

How-many-integers-between-999-and-4000-both-are-included-can-be-formed-using-digits-0-1-2-3-4-if-repetition-of-digits-is-allowed-

Question Number 130034 by EDWIN88 last updated on 22/Jan/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{integers}\:\mathrm{between}\:\mathrm{999}\:\mathrm{and}\:\mathrm{4000} \\ $$$$\left(\mathrm{both}\:\mathrm{are}\:\mathrm{included}\right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using} \\ $$$$\mathrm{digits}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{if}\:\mathrm{repetition}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{is} \\ $$$$\mathrm{allowed}?\: \\ $$ Answered by liberty last updated on 22/Jan/21…

The-surnames-of-40-students-in-a-class-were-arranged-in-alphabetical-order-16-of-the-surnames-begin-with-O-while-9-of-the-surnames-begin-with-A-14-of-the-letters-of-the-alphabet-do-not-appear-as-t

Question Number 63596 by Tawa1 last updated on 05/Jul/19 $$\mathrm{The}\:\mathrm{surnames}\:\mathrm{of}\:\mathrm{40}\:\mathrm{students}\:\mathrm{in}\:\mathrm{a}\:\mathrm{class}\:\mathrm{were}\:\mathrm{arranged}\:\mathrm{in} \\ $$$$\mathrm{alphabetical}\:\mathrm{order}.\:\mathrm{16}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{O}\:\mathrm{while} \\ $$$$\mathrm{9}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{A}.\:\:\mathrm{14}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{alphabet}\:\mathrm{do}\:\mathrm{not}\:\mathrm{appear}\:\mathrm{as}\:\mathrm{the}\:\mathrm{first}\:\mathrm{letter}\:\mathrm{of}\:\mathrm{any}\:\mathrm{surname}. \\ $$$$ \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surname}\:\mathrm{of}\:\mathrm{a}\:\mathrm{child}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{the}\:\mathrm{class}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{either}\:\mathrm{A}\:\mathrm{or}\:\mathrm{O} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{If}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one}\:\mathrm{surname}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{a}\:\mathrm{letter}\:\mathrm{besides}\:\mathrm{A} \\…

Arrange-these-digits-1-1-2-2-3-3-4-4-So-that-the-1-s-are-four-digit-apart-So-that-the-2-s-are-three-digit-apart-So-that-the-3-s-are-two-digit-apart-So-that-the-4-s

Question Number 63246 by Tawa1 last updated on 01/Jul/19 $$\mathrm{Arrange}\:\mathrm{these}\:\mathrm{digits}:\:\:\:\:\:\:\mathrm{1}\:\:\mathrm{1}\:\:\mathrm{2}\:\:\mathrm{2}\:\:\mathrm{3}\:\:\mathrm{3}\:\:\mathrm{4}\:\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{1}'\mathrm{s}\:\mathrm{are}\:\mathrm{four}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{2}'\mathrm{s}\:\mathrm{are}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{3}'\mathrm{s}\:\mathrm{are}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{4}'\mathrm{s}\:\mathrm{are}\:\mathrm{one}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$ \\ $$ Commented by mr…