How many ways can the president be picked ?.

Probability Level 3

There are 10 persons working in a company. The management team comprises of any 4 persons selected at random from the 10 persons. Any one person from the management team is appointed as the President of the company. In how many ways can the President be picked ?

210 4 10 840

Srinivasa Gopal by Srinivasa Gopal , 53, India

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2 solutions

Srinivasa Gopal
Jul 18, 2019

Number of ways 4 persons can be selected from 10 is equal to 10c4 = 210 Number of ways one person out of the 4 can be selected as President is equal to 4c1 = 4 Total number of ways of selecting any 4 persons to form the committee and then select one of them as the President is equal to 210 * 4 = 840

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And President will be 1 of 10 so 10 ways

Hasmik Garyaka - 1 year, 10 months ago

What you are suggesting is related to probability, the question is about counting using permutations and combinations.

Srinivasa Gopal - 1 year, 10 months ago

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No. You should formulate problem so - in how many ways we can select President and management. But President is one of 10.

Hasmik Garyaka - 1 year, 10 months ago

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If A1, A2, A3.. A10 are the 10 persons who are working in the office. The committee of 4 may be picked as A3,A4,A9,A10 , the president may be A3, A4,A9,A10 giving us the permutations as A3,A4,A9,A10 - A3 or A3,A4,A9,A10 - A4 or A3,A4,A9,A10 - A9 or A3,A4,A9,A10 - A10. Since 4 from 10 can be picked in 210 ways I have a total of 4 * 210 permutations. If the question was how many ways can we select 1 person as a president from an office of 10 persons , then 10 c 1 = 10 is correct. But we are selecting a committee of 4 first then a president as one of the 4.

Srinivasa Gopal - 1 year, 10 months ago

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@Srinivasa Gopal – Its the same I said. Change the problem.

Hasmik Garyaka - 1 year, 10 months ago

Maybe the question ought to specify that it's asking for the number of ways in which this entire process could occur. There are only ten ways to "pick a president" in that there are only ten possible results. As it is currently stated, the questions seems ambiguous.

Tristan Goodman - 1 month, 1 week ago
Richard Desper
Jul 18, 2019

Alternatively: there are 10 possible Presidents, and for each President there are 9C3 possible groups of 3 that comprise the rest of the committee. 9C3 = 84, so there are 840 ways in total to select a President.

As often is the case with counting problems, there are different ways to formulate an approach that (hopefully) end up with the same result.

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