One-third of 15 mangoes got rotten. If 5 mangoes are taken out randoml

1.	One-third of 15 mangoes got rotten. If 5 mangoes are taken out randomly, what is the probability that no mango is rotten?1). 12/1432). 12/1333). 16/994). 85/99
Answer» One-third of 15 mangoes got rotten Rotten mangoes = 15/3 = 5 So, number of good mangoes = 15 – 5 = 10 When 5 mangoes are taken out RANDOMLY, the probability that no mango is rotten = ¹⁰C₅/¹⁵C₅ $(= {\rm{\;}}\frac{{10!}}{{5! \times 5!\;}}\; \times \frac{{5! \times 10!}}{{15!}} = \frac{{10! \times 10!}}{{15! \times 5!}})$ $(= {\rm{\;}}\frac{{10 \times 9 \times 8 \times 7 \times 6 \times 5! \times 10!}}{{15 \times 14 \times 13 \times 12 \times 11 \times 10! \times 5!}})$ $(= {\rm{\;}}\frac{{10 \times 9 \times 8 \times 7 \times 6}}{{15 \times 14 \times 13 \times 12 \times 11}})$ = 12/(11×13) = 12/143

One-third of 15 mangoes got rotten. If 5 mangoes are taken out randomly, what is the probability that no mango is rotten?1). 12/1432). 12/1333). 16/994). 85/99

Answer»

One-third of 15 mangoes got rotten

Rotten mangoes = 15/3 = 5

So, number of good mangoes = 15 – 5 = 10

When 5 mangoes are taken out RANDOMLY, the probability that no mango is rotten = ¹⁰C₅/¹⁵C₅

$(= {\rm{\;}}\frac{{10!}}{{5! \times 5!\;}}\; \times \frac{{5! \times 10!}}{{15!}} = \frac{{10! \times 10!}}{{15! \times 5!}})$

$(= {\rm{\;}}\frac{{10 \times 9 \times 8 \times 7 \times 6 \times 5! \times 10!}}{{15 \times 14 \times 13 \times 12 \times 11 \times 10! \times 5!}})$

$(= {\rm{\;}}\frac{{10 \times 9 \times 8 \times 7 \times 6}}{{15 \times 14 \times 13 \times 12 \times 11}})$

= 12/(11×13)

= 12/143

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