A bag contains two red balls, two green balls, two white balls, two black balls and two yellow balls. Other than the colour, the balls are all indistinguishable. Find the number of different ways in which a selection of 5 balls can be made

Question

A bag contains two red balls, two green balls, two white balls, two black balls and two yellow balls. Other than the colour, the balls are all indistinguishable. Find the number of different ways in which a selection of 5 balls can be made (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/0380fed37ae1099c960c60bdb87d563e-.png" /> (i) 2 alike +3 different = 5 C 1 ⋅ 4 C 3=20 (ii) 2 alike +2 other alike +1 different = 5 C 2 ⋅ 3=30 (iii) all five different =1 Total =51

Q. A bag contains two red balls, two green balls, two white balls, two black balls and two yellow balls. Other than the colour, the balls are all indistinguishable. Find the number of different ways in which a selection of 5 balls can be made

(i) 2 alike +3 different
$=^{5} C_{1} \cdot^{4} C_{3} = 20$
(ii) 2 alike +2 other alike +1 different
$=^{5} C_{2} \cdot 3 = 30$
(iii) all five different $= 1$
Total $= 51$

Q. A bag contains two red balls, two green balls, two white balls, two black balls and two yellow balls. Other than the colour, the balls are all indistinguishable. Find the number of different ways in which a selection of 5 balls can be made

(i) 2 alike +3 different =5C1​⋅4C3​=20 (ii) 2 alike +2 other alike +1 different =5C2​⋅3=30 (iii) all five different =1 Total =51

(i) 2 alike +3 different
$=^{5} C_{1} \cdot^{4} C_{3} = 20$
(ii) 2 alike +2 other alike +1 different
$=^{5} C_{2} \cdot 3 = 30$
(iii) all five different $= 1$
Total $= 51$