How many ways can the letter of the word oranges be arranged?

How many different words can be formed with the letters of the word ORANGE, with vowels occupying odd places?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Suggest Corrections

Take note of the word "surprising":There are 10 letters total.There are 2 r's.There are 2 i'sThere are 2 s's.There are 10! total ways to arrange the letters. Since repetition is not allowed for the arrangements, we need to divide the total number of arrangements by 2!2!2! Therefore, you should get 10!/(2!2!2!) distinct arrangements

How many ways can the letters of the word ORANGES be arranged. 11. if there are no restrictions?
A.
B.
C.
D. 12. if the first letter must be an N?
A.
B.
C.
D. 13. In how many ways can the organizer of the Sinulog Festival arrange the first three performers if there are contingents in all?
A.
B.
C. D.

Distinguishable Ways to Arrange the Word ORANGE
The below step by step work generated by the word permutations calculator shows how to find how many different ways can the letters of the word ORANGE be arranged.

Objective: Find how many distinguishable ways are there to order the letters in the word ORANGE.

Step by step workout:

step 1 Address the formula, input parameters and values to find how many ways are there to order the letters ORANGE.
Formula:
nPr =n!/(n1! n2! . . . nr!)

Input parameters and values:

Total number of letters in ORANGE: n = 6 Distinct subsets: Subsets : O = 1; R = 1; A = 1; N = 1; G = 1; E = 1; Subsets' count:

n1(O) = 1, n2(R) = 1, n3(A) = 1, n4(N) = 1, n5(G) = 1, n6(E) = 1

step 2 Apply the values extracted from the word ORANGE in the (nPr) permutations equation

nPr = 6!/(1! 1! 1! 1! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6/{(1) (1) (1) (1) (1) (1)}

= 720/1

= 720 nPr of word ORANGE = 720 Hence, The letters of the word ORANGE can be arranged in 720 distinct ways.

Apart from the word ORANGE, you may try different words with various lengths with or without repetition of letters to observe how it affects the nPr word permutation calculation to find how many ways the letters in the given word can be arranged.