Question

A box contains 10 coupons, labelled as 1,2,.....10.Three coupons are drawn at random and without X1,X2 and X3 denote the numbers on the coupons. Then the probability that max{X1,X2,X3}<7 is

• A. $\dfrac{3C_1}{10C_3}$
• B. $\dfrac{7C_3}{10C_3}$
• C. $\dfrac{3C_3}{10C_3}$
• D. $\dfrac{3C_1}{10C_7}$
• E. $\dfrac{6C_3}{10C_3}$

Answer 1

Answer: (E)

$\dfrac{6C_3}{10C_3}$

Answer 2

Given Data:

Total no of coupons = $10$ (labelled as 1,2,.....10)

Three coupons are drawn at random and without replacement.

To find probability of max {X1,X2,X3}$<7$

Proceeding according to the question, drawing $3$ coupons out of $10$ =$10C_3$

Now, let's count the number of favorable outcomes (max{X1, X2, X3} < 7).

For max {X1, X2, X3} to be less than $7$, all three coupons X1, X2, and X3 must have values less than $7$ and there are $6$ coupons (1 to 6) that fulfills the condition.

So, drawing $3$ coupons out of these $6$ coupons =$6C_3$

Now , Probability=$\dfrac{PE}{TE}$ (⇢ Possible events/Total events)

                       = $\dfrac{6C_3}{10C_3}$ (_Ans.)