Multiple choice

A bag contains $9$ balls marked with digit $1, 2, ......9$. If two balls are drawn from the bag, then numbers of ways getting the sum of the digits on balls as $10$

  1. $8$
  2. $2^9$
  3. $^9C_2$
  4. $^9P_2$
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A Correct answer
Explanation

We need to find pairs (a, b) from {1, 2, ..., 9} such that a + b = 10 and a is not equal to b. The pairs are (1,9), (2,8), (3,7), (4,6), (6,4), (7,3), (8,2), (9,1). There are 8 such ways.