A bag contains $$10$$ balls of which $$2$$ are red and the remaining are either blue or black. If the probability drawing $$3$$ balls of the same colour is $$1120$$ and if the number of blue balls exceeds the number of black balls, the number of blue balls is

Question

A bag contains $$10$$ balls of which $$2$$ are red and the remaining are either blue or black. If the probability drawing $$3$$ balls of the same colour is $$1120$$ and if the  number of blue balls exceeds the number of black balls, the number of blue balls is

Infinity Learn · Accepted Answer

Let the number of blue balls be n. ∴  the number of black balls $$=10$$−(n+2)=8$$−n.  If all the three balls drawn are of the same colour, they must  be either blue or black,  the probability for which is  $$nC3$$ $$10C3+$$ $$8$$−$$nC3$$ $$10C3=11120$$⇒ $$n(n$$−$$1)(n$$−$$2)+(8$$−$$n)(7$$−$$n)(6$$−$$n) $$=10$$×$$9$$×$$8$$⋅$$11120$$⇒ $$18n2$$−$$144n+336=66$$⇒ $$n2$$−$$8n+15=0$$⇒ (n$$−$$5)(n$$−$$3)=0$$⇒ $$n=5$$ $$(as$$ n> number of black $$balls)

Theorems of probability

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A bag contains 10 balls of which 2 are red and the remaining are either blue or black. If the probability drawing 3 balls of the same colour is $\frac{11}{20}$ and if the number of blue balls exceeds the number of black balls, the number of blue balls is

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Theorems of probability

Remember concepts with our Masterclasses.

A bag contains 10 balls of which 2 are red and the remaining are either blue or black. If the probability drawing 3 balls of the same colour is 1120 and if the number of blue balls exceeds the number of black balls, the number of blue balls is

Ready to Test Your Skills?

free study material

A bag contains 10 balls of which 2 are red and the remaining are either blue or black. If the probability drawing 3 balls of the same colour is $\frac{11}{20}$ and if the number of blue balls exceeds the number of black balls, the number of blue balls is