The no. of ways to select the 3 blue balls and 5 orange balls from the urn is 0.424
No. of Blue balls in the urn = 5
No. of Orange balls in the urn = 7
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 5 + 7
= 12 balls
No. of blue balls to be selected = 3
No. of orange balls to be selected = 5
No. of balls to be selected = 8
The total. no of ways 8 balls can be selected = 12C₈
The No. of ways 3 blue balls can be selected = 5C₃
The No. of ways 5 orange balls can be selected = 7C₅
Therefore, No. of ways to select 3 blue balls and 5 orange balls from the urn
= 5C₃ x 7C₅ / 12C₈
[ Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls]
P = 10 x 21 / 495
= 210 / 495
P = 0.424
Therefore, the no. of ways to select blue and orange balls is 0.424
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