Find the number of ways to purchase 5 different kinds of juices from a selection of 10 juices.

Solution:

Given, there are 10 different kinds of juices.

We have to purchase 5 different kinds of juices from a selection of 10 juices.

By using the formula for combinations:

The number of ways = n!/(r!(n - r)!)

Here, n= 10 and r = 5

Number of ways = 10!/(5!(10 - 5)!)

It can be written as

= (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/[(5 × 4 × 3 × 2 × 1)(5!)

= 3628800/[(120) × (5 × 4 × 3 × 2 × 1)]

By further calculation

= 3628800/[120 × 120]

So we get

= 30240/120

= 252 ways

Therefore, there are 252 ways to purchase 5 different kinds of juices.

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Find the number of ways to purchase 5 different kinds of juices from a selection of 10 juices.

Summary:

The number of ways to purchase 5 different kinds of juices from a selection of 10 juices is 252 ways.