Question

10 balls are picked from a pile of red,blue and white balls.how many such a selections contain less than 5 red balls ​

Answer 1

Answer:

There are 47 balls of which 20 are red, 15 blue and 12 green. Or, in other words, there are 20 red balls and 27 not-red balls.

Now, 10 balls can be selected from these 47 balls in ways. …( 1 ).

Again, selection of at least 4 red balls means 4 or more red balls. Complimentary of this is the selection of at most 3 red balls which means that there are 3 or less red balls which gives rise to following 4 cases — (i) selection 10 balls out of all 27 non-red balls (ii) selection of 1 red ball out of 20 and 9 non-red balls out of 27 (iii) selection of 2 red balls and 8 non-red balls & (iv) selection of 3 red balls and 7 non-red balls. So, the numbers of such selections are ( 2)

Hence, required number of selection of 10 balls having at least 4 red balls is (1)-(2)