First slide

Theorems of probability

Question

$Let the 9 different letters A, B, C, \dots, I \in {1, 2, 3, \dots 9} then the probability that product (A - 1) (B - 1) \dots (I - 9)$ $is even number will be$

Moderate

A

$\frac{1}{2}$
B

$\frac{1}{4}$
C

1
D

0

Solution

Given set of numbers is {1,2, ...,9} in which 4 are even and 5 are odd, so in the given product it is not possible
to arrange to substract only even number from odd number, there must be at least one factor involving subtraction of an odd
number from another odd number. So, at least one of the factor is even. Hence product is always even.
.'. Required Probability = 1

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