Question

What is the total number of ways of selecting 10 balls from unlimited supply of red , black and white and green balls ?

Answer 1

Pikaa 

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♦ Permutation Combination ♦

  ◘ We are basically counting for 40 balls, 10 each, instead of the 'unlimited' term which is somewhat meant for confusion 

 ◘ Simplifying the problem, we seek for the positive integer solution for : 
     $n_{red} + n_{black} + n_{white} + n_{green} = 10$ 
  • Why ? 

♦ Number of integral solutions of x₁ + x₂ + ... + xₐ = n is given as :
    • $^{n+a-1}C_{a-1}$

Hence, the solution subjects to finding : C( 10 + 4 - 1 , 4 - 1 ) = C( 13 , 3 ) 

◙ Finally, we have, the number of ways in which 10 four color balls can be selected out of unlimited stock is : 286 

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For further reference,
 
'https://www.careerbless.com/aptitude/qa/permutations_combinations_imp8.php'  

'https://math.stackexchange.com/questions/411349'

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Hope this helps