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Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > From 4 officers and 8 jawans, In how many ways can...
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From 4 officers and 8 jawans, In how many ways can 6 be chosen so as to essentially include at least one officer ?

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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

total number of ways for selecting 6 persons out of 8 officers and 4 jawans are (i) 1 Officer and 5 jawans (ii) 2 Officers and 4 jawans (iii) 3 Officers and 3 jawans (iv) 4 Officers and 2 jawans 4C1. 8C5 + 4C2.8C4 + 4C3.8C3 + 4C4.8C2 = 224 + 420 + 224 + 28 = 896
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Tutor

The required cases of at least one officer = total cases - cases having only jawans = 12C6 - 8C6 = 924 - 28 = 896.
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Trainer

Solution: (4C1 x 8C5) + (4C2 x 8C4)+(4C3 x 8C3)+(4C4 x 8C2) ways
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Aptitude for Placement, Bank, B. Tech Subjects, M. Tech subjects and Projects (ECE, CSE, IT, EEE), Net for ELectronics

12C6 - 8C6
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224
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12C6 - 8C6
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Native English Speaker with 32 years experience in teaching English and communication skills.

12c6 - 8c6 = 896
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Trainer

896
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GMAT Math Expert

12C6 - 8C6
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GMAT Math Expert

12C6 - 8C6.. 1st I have selected 6 people out of 12 people (4 officers and 8 jawans) in 12C6 ways. We can select all 6 Jawans in 8C6 ways. However, we want atleast one officer. So it's 12C6-8C6 ways.
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