Committee X has 4 members, committees Y has 5 members, and these committees have no members in common. If a task force is to be formed consisting of one member of X and one member of Y, how many different task forces are possible?

প্রশ্নে বলা হচ্ছে যে, x কমিটিতে 4 জন এবং y কমিটিতে 5 জন সদস্য রয়েছে। ঐ দুটি কমিটিতে x এবং y এর কোনো সাধারণ সদস্য নেই। এখন x  থেকে 1 জন এবং y থেকে 1 জন নিয়ে একটি কমিটি গঠন করা হলে কতভাবে কমিটি গঠন করা যাবে?

এখানে, 4 জন হতে 1 জনকে ⁴ C₁ = 4 উপায়ে বাছাই করা যায়।
আবার, 5 জন হতে 1 জনকে ⁵C₁ = 5 উপায়ে বাছাই করা যায়।
নির্ণেয় উপায়সংখ্যা = 4 × 5 = 20 উপায়ে।

To form a task force consisting of one member of X and one member of Y, you can use the concept of combinations. Since committee X has 4 members and committee Y has 5 members, you have choices for selecting one member from each committee.

The number of different task forces possible is the product of the number of ways you can choose one member from each committee.

Number of ways to choose one member from X = C(4, 1) = 4 (choose 1 from 4) Number of ways to choose one member from Y = C(5, 1) = 5 (choose 1 from 5)

Total number of different task forces = 4 (from X) * 5 (from Y) = 20

So, there are 20 different task forces possible.