A lady gives a dinner party for six guests. In how many ways they be selected from among 10 friends

The problem can be solved using the concept of combinations in mathematics.

A combination is a selection of items without considering the order. In this case, the lady is selecting 6 guests out of 10 friends, and the order in which they are selected does not matter.

The formula for combinations is:

C(n, r) = n! / [(n-r)! * r!]

where:

• n is the total number of items,
• r is the number of items to select,
• "!" denotes factorial, which is the product of all positive integers up to that number.

Substituting the given values into the formula:

C(10, 6) = 10! / [(10-6)! * 6!]

= 10987654321 / [(4321) * (65432*1)]

After simplifying, we find that the lady can select 6 guests out of 10 friends in 210 different ways.