MCQ
Three integers are chosen at random from the first 20 integers. The probability that their product is even is:
- A$\frac{2}{19}$
- B$\frac{3}{29}$
- C$\frac{17}{19}$
- D$\frac{4}{19}$
Three integers are chosen at random from the first 20 integers. The probability that their product is even is:
Solution:
Number of ways in which we can choose three distinct integers from 20 integers
$\ ^{20}\text{C}_3=1140$We know that, if we take three odd numbers, there product will always be an odd number.
Out of 20 consecutive integers, 10 are even and 10 are odd integers.
Number of ways in which we can choose three distinct odd integers from 10 odd integers $=\ ^{10}\text{C} _3=120$
P(product is even) = 1 - P(product is odd),
$=1-\frac{120}{1140}=\frac{1140-120}{1140}=\frac{1020}{1140}=\frac{17}{19}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
The total number of terms in the expansion of $(\text{x}+\text{a})^{100}+(\text{x}-\text{a})^{100}$ after simplification is:
The distance between (6, 5) and (-3, 4) is:
Choose the correct answer.
A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is: