Question

Salman khan has 10 different shirts, 5 different trousers, five different tie, three different shoes.In how many ways he can wear them if

1) wearing all items are compulsory.
2) wearing shirt and trousers are compulsory​

Answer 1

Explanation:

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Answer 2

Answer:

1) 750 ways he can wear them if wearing all items are compulsory.

2) 1200 ways he can wear them if wearing shirt and trousers are compulsory​

Explanation:

• It is given that, Salman khan has 10 different shirts, 5 different trousers, five different tie, three different shoes.

• For each shirt 5 different trousers can be worn. That makes 10 × 5 = 50 different outfits, with a different combination of a shirt and trousers.

• Now for each shirt and trousers combination, 3 pairs of shoes can be worn. That would make a total of 50 x 3 = 150 different combinations of outfits.

• Now for each shirt ,trousers and shoes combination, 5 ties can be worn.

        Hence,  the total combinations that can be made = 150 x 5 = 750

(1) Therefore he can wear 10 different shirts, 5 different trousers, five different tie, three different shoes in 750 different ways.

(2) Number of combinations if wearing shirt and trousers are compulsory​

• If he includes 1 shirt, 1 trouser , 1 tie, 1 pair of shoe , then there are 750 combination,

• If he includes 1 shirt, 1 trouser , 1 tie, then there are 10×5 × 5 = 250 combinations.
• If he includes 1 shirt, 1 trouser , 1 shoes, then there are 10×5 × 3 = 150 combinations.
• If he includes 1 shirt, 1 trouser  then there are 10 × 5 = 50 combination,

Hence the total possible combination for outfits if wearing shirt and trousers are compulsory​ = 750 + 250 + 150 + 50 = 1200.

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