How-many-ways-can-the-letters-in-the-word-MATHEMATICS-be-rearranged-such-that-the-word-formed-neither-starts-nor-ends-with-a-vowel-and-any-four-consecutive-letters-must-contain-at-least-a-vowel- Tinku Tara June 4, 2023 Permutation and Combination 0 Comments FacebookTweetPin Question Number 110729 by mr W last updated on 30/Aug/20 HowmanywayscanthelettersinthewordMATHEMATICSberearrangedsuchthatthewordformedneitherstartsnorendswithavowel,andanyfourconsecutivelettersmustcontainatleastavowel? Answered by mr W last updated on 30/Aug/20 (seealsoQ110498)n1n2n3n4n5=voweln1…5=numberofconsonants1⩽n1,n5⩽30⩽n2,n3,n4⩽3n1+n2+n3+n4+n5=7ingeneratingfunction(x+x2+x3)2(1+x+x2+x3)3=x2(1+x+x2)2(1+x+x2+x3)3=x2(1−x3)2(1−x4)3(1−x)5=x2(1−x3)2(1−x4)3∑∞k=0C4k+4xkthecoefficientofx7termis:C45+4−2×C42+4−3×C41+4=81⇒81×7!2!2!×4!2!=1224720ways Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: To-the-developer-of-tinkutara-Sir-since-yesterday-the-app-crashes-when-i-go-for-any-page-other-than-the-main-sort-by-question-id-page-please-help-my-phone-is-2G-compatible-android-old-version-Next Next post: kojo-can-do-a-piece-of-work-in-5hours-Edina-can-do-the-same-work-in-4hours-how-long-will-it-take-the-two-of-them-to-do-the-same-work-together-if-they-work-at-the-same-rate- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.