If four pencils are picked at random, what is the

Solution

Total number of pencils = 6 + 4 + 2 +4 = 16 Let S be the sample space. Then, n(S) = total number of ways of drawing 4 pencils out of 16 = 16C4[if gte msEquation 12]>¹⁶ C 4 [if !msEquation]--> [endif]--> = `(16xx15xx14xx13)/(4xx3xx2xx1)` [if gte msEquation 12]>   16 × 15 × 14  × 13 4 × 3 × 2 × 1 [if !msEquation]--> [endif]--> = 1820 Let E= event of drawing 4 pencils when none is of same colour. n(E) = 6C1 X 4C 1 X 2C1 X 4C1 = `6xx4xx2xx4 = 192` [if gte msEquation 12]>∴ [if !msEquation]--> [endif]--> P (E) when none is of same colour = `192/1820` [if gte msEquation 12]> 192 1820 [if !msEquation]--> [endif]--> [if gte msEquation 12]>∴ [if !msEquation]--> [endif]--> P (E) when at least two are of same colour= 1 - `192/1820 = 1628/1820 = 407/455` [if gte msEquation 12]> 192 1820 [if !msEquation]--> [endif]-->