Question

From a box containing 10 cards numbered 1 to10, four cards are drawn together. The probability that their sum is odd is

• A. $\frac{1}{2}$
• B. $\frac{11}{21}$
• C. $\frac{10}{21}$
• D. $\frac{1}{21}$

Answer 1

The correct option is C $\frac{10}{21}$

The only way of getting a odd sum is by choosing only one odd number out of 4 cards or choosing 3 odd numbers out of 4 cards chosen.The number of ways it can be done is ${}^5{C}_1{\times }^5{C}_3{+}^5{C}_3{\times }^5{C}_1$
$=100$
The total number of ways in which 4 cards can be chosen are :
${}^{10}{C}_4=210$
So probability is $100/210=10/21$