Out-of-5-accountants-and-7-bankers-a-committee-consisting-of-2-accountants-and-3-bankers-is-to-be-formed-In-how-many-ways-can-this-be-done-if-a-Any-acountant-and-any-bankers-must-be-included-b-

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Question Number 11384 by tawa last updated on 22/Mar/17

$$\mathrm{Out}\mathrm{of}5\mathrm{accountants}\mathrm{and}7\mathrm{bankers},\mathrm{a}\mathrm{committee}\mathrm{consisting}\mathrm{of}$$$$2\mathrm{accountants}\mathrm{and}3\mathrm{bankers}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{formed}.\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{ways}\mathrm{can}\mathrm{this}$$$$\mathrm{be}\mathrm{done}\mathrm{if}$$$$\left(\mathrm{a}\right)\mathrm{Any}\mathrm{acountant}\mathrm{and}\mathrm{any}\mathrm{bankers}\mathrm{must}\mathrm{be}\mathrm{included}$$$$\left(\mathrm{b}\right)\mathrm{One}\mathrm{particular}\mathrm{banker}\mathrm{must}\mathrm{be}\mathrm{included}$$$$\left(\mathrm{c}\right)2\mathrm{accountant}\mathrm{cannot}\mathrm{be}\mathrm{in}\mathrm{the}\mathrm{committee}$$

Answered by sandy_suhendra last updated on 23/Mar/17

$$\left(\mathrm{a}\right)4\mathrm{C}1\times 6\mathrm{C}2=4\times 15=60$$$$\left(\mathrm{b}\right)5\mathrm{C}2\times 6\mathrm{C}2=10\times 15=150$$$$\left(\mathrm{c}\right)3\mathrm{C}2\times 7\mathrm{C}3=3\times 35=105$$

Commented by tawa last updated on 23/Mar/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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