The number of ways of selecting atleast one red ball from a bag containing $4$ identical red balls and $5$ identical black balls is

Since the 4 red balls and 5 black balls are identical, the number of ways to choose at least one red ball depends on how many red balls you pick. You can choose 1, 2, 3, or 4 identical red balls, giving 4 options. For each of these choices, you can independently choose to include 0, 1, 2, 3, 4, or 5 identical black balls, which gives 6 options. Multiplying these independent choices gives 4 times 6, resulting in 24.

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