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A-party-of-7-members-is-to-be-chosen-from-a-group-of-6-ladies-and-5-gents-In-how-many-ways-can-the-party-be-formed-if-it-is-to-contain-i-exactly-4-ladies-i-at-least-4-ladies-i-at




Question Number 6098 by Rasheed Soomro last updated on 13/Jun/16
A party of  7   members is to be chosen  from a group of  6  ladies and  5  gents.  In how many ways can the party be  formed if it is to contain  (i)   exactly 4  ladies  (i)   at least 4  ladies  (i)   at most 4  ladies ?
$$\mathrm{A}\:\mathrm{party}\:\mathrm{of}\:\:\mathrm{7}\:\:\:\mathrm{members}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{chosen} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{group}\:\mathrm{of}\:\:\mathrm{6}\:\:\mathrm{ladies}\:\mathrm{and}\:\:\mathrm{5}\:\:\mathrm{gents}. \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{party}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{to}\:\mathrm{contain} \\ $$$$\left(\mathrm{i}\right)\:\:\:\mathrm{exactly}\:\mathrm{4}\:\:\mathrm{ladies} \\ $$$$\left(\mathrm{i}\right)\:\:\:\mathrm{at}\:\mathrm{least}\:\mathrm{4}\:\:\mathrm{ladies} \\ $$$$\left(\mathrm{i}\right)\:\:\:\mathrm{at}\:\mathrm{most}\:\mathrm{4}\:\:\mathrm{ladies}\:? \\ $$

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