Mathematics Test - 10

Here, we have 1 M, 4 I's, 4 S's and 2 P's,

Hence, the total number of different combinations of letters of the word MISSISSIPPI are11!/41 x 41 x2! .

Required number = 2 x ²⁰C₂ because if A sends to B, then B also sends to A, so it becomes twice for all.

Out of 9 men, 2 men can be chosen in ⁹C₂ ways.

Since no husband and wife are to play in the same game, we have to select 2 women from the remaining 7 women.

This can be done in ⁷C₂ ways.

If M₁, M₂ and W₁, W₂ are chosen, then a team can be constituted in 2 ways, viz. M₁ W₁ or M₁ W₂.

Thus, number of ways of arranging the game = ⁹C₂ x ⁷C₂ x 2 = 1512

Since, the number of faces is the same as the number of colours, and the faces are identical, therefore, the number of ways of painting them is 1.

Considering AU as one letter, we have 4 letters: L, AU, G, H, which can be permuted in 4! ways. But, AU can be put together in 2! ways. Thus, the required number of arrangements is 4! × 2! = 48.

Starting with the letter A and arranging the other four letters, there are 4 ! = 24 words. These are the first 24 words. Then, starting with G and arranging A, A, I and N in different ways, there are = 4!/2! 1! 1! = 24/2 = 12 words

Next, the 37^th word starts with I. There are 12 words starting with I.

This accounts up to the 48^th word.

The 49^th word is NAAGI.

The 50^th word is NAAIG.

Here, the order of the couples is not important. So, required number of ways is 20!/2¹⁰10!