Answer

Verified

414.3k+ views

**Hint:**In this question combination formula will be used for getting a suitable group. There will be possibly four cases consisting of different varieties of groups of men and ladies. Final answer will be the total of all four cases.

**Complete step-by-step answer:**

Here, Friends of X = 4 Ladies + 3 Men

Friends of Y = 3 Ladies + 4 Men

Case-1: When 3 ladies from X and 3 men from Y will be invited.

So, no. of ways =

$

C(4,3) \times C(4,3) \\

= 4 \times 4 \\

= 16 \\

$

Case-2: When 2 ladies from X and 1 lady from Y will be invited with 1 man from X and 2 men from Y.

So, no. of ways =

$

C(4,2) \times C(3,1) \times C(3,1) \times C(4,2) \\

= 6 \times 3 \times 3 \times 6 \\

= 324 \\

$

Case-3: When 1 lady from X and 2 ladies from Y, and from 2 men from X and 1 man from Y will be invited.

So, no. of ways =

$

C(4,1) \times C(3,2) \times C(3,2) \times C(4,1) \\

= 4 \times 3 \times 3 \times 4 \\

= 144 \\

$

Case-4: When 0 lady from X means 3 men from X and 3 ladies from Y will be invited.

So, no. of ways =

$

C(3,3) \times C(3,3) \\

= 1 \times 1 \\

= 1 \\

$

$\therefore $ Total number of ways will be = 16 + 324 + 144 + 1

= 485

**Note:**Probability is the possible number of outcomes to the total number of outcomes. Permutations is the arrangement of the items in the set. Combinations is the selection of items from the total number of items in a set.

Recently Updated Pages

Differentiate between Shortterm and Longterm adapt class 1 biology CBSE

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE