on how many nights may a watch of four men be drafted from a crew of 24 so that no two watches are identical. on how many of these would one man be taken?

Dear manisha

the number of ways in ²⁴C₄  = 10626 .

When a perticular man is to be always included then we need to select 3 men out of 23.so total ways = ²³C₃ = 1771

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Badiuddin

I have got the answer , so i am sharing with u, its very-∞ easyPart - 1For How many nights24C4 =24 x 23 x 22 x 21/4!=10626.BecauseEach of the groups or selections which can be made by takingsome or all of a number of things is called a combination.Thus the •permutations which can be made by taking theletters a, b, c, d two at a time are twelve in number, namely,ab, ac, ad, be, bd, cd,ba, ca, da, cb, db, dc;each of these presenting a different arrangement of two letters.The combinations which can be made by taking the lettersa, b, c, d two at a time are six in number : namely,ab, ac, ad, be, bd, cd;each of these presenting a different selection of twoafter reading the above underlined sentence you would be able to understand that why i ve used Combination formula to get the answer as in our question by using the formulae of combination we will get Different Selection of watchmen so that no two watches are identical.Part - IIWhen a perticular man is to be always included then we need to select 3 men out of 23.so total ways = 23C3 = 1771.If you understand this answer please like